The author of Matthew was definitely not an annihilationist, i.e. viewing divine judgment in an OT sense consisting of a single moment of destruction. He viewed destruction in Gehenna as a sustained torment over the same duration the righteous receive eternal life. Check out Sim’s book where he lays out all the evidence for the author’s eschatology which is the closest to that in 1 Enoch found in the NT. The language in Matthew 10:28 is consistent with this. Soul and body (ψυχὴν καὶ σῶμα) indicates that the evildoers are embodied when they are dispatched to Gehenna, i.e. following their judgment after the resurrection (cf. Daniel 12:2-3 picturing judgment with rewards and punishments following the resurrection, the language being exegetical of Isaiah 66:24 which is the source text on the concept of Gehenna). This is no longer the mere burning of corpses (as it is in the original passage in Trito-Isaiah) but the burning of embodied souls capable of feeling pain, who weep and gnash their teeth (Judith 16:17; cf. Matthew 8:12, 13:42, 50, 22:13, 24:51, 25:30).
As for ἀπόλλυμι, this does not imply annihilation to the exclusion of eschatological torment. It is part of the traditional OT language of divine judgment and was thus recruited in apocalypses which refer to torment as a penalty of the Last Judgment. According to George Nickelsburg, ἀπόλλυμι and ἀπώλεια (with their Aramaic equivalents) are technical terms in 1 Enoch for damnation after judgment (Hermeneia commentary on 1 Enoch, pp. 161, 457). The most famous instance is in the Book of Watchers: “Behold, he comes with the myriads of his holy ones to execute judgment on all, and to destroy all the wicked (ἀπολέσει πάντας τοὺς ἀσεβεῖς), and to convict all flesh, for all the wicked deeds that they have done, and the proud and hard words that wicked sinners spoke against him” (1:9; interestingly this verse combines OT language from Jeremiah 25:30-31 and Isaiah 66:15-16, the latter just a few verses before Isaiah 66:24). The concept is not of annihilation on Judgment Day but an enduring damnation with torments. We read in the verdict of the sinners’ judgment in 5:5 that “the years of your destruction (τὰ ἔτη τῆς ἀπωλείας ὑμῶν) will increase in an eternal curse (κατάρᾳ αἰώνων), and there will be no mercy or peace to you”. This is a destruction that lasts years stretching into eternity and this is a destruction that is experienced by the sinners without peace; annihilation would be merciful in comparison. So Matthew’s use of ἀπολέσαι is quite consistent with his apocalyptic heritage.
Both 1 Enoch and Matthew, the work that actually uses the phrase “eternal punishment” (κόλασιν αἰώνιον) in 25:46. In 1 Enoch (at least outside of the Book of Parables, the latest addition to the corpus), the idea isn’t that divine judgment brings permanent death in a moment of destruction without torture or a perpetual punishment. Rather it portrays destruction as a lasting condition experienced by evildoers as torment.
(1) The verdict of the judgment on evildoers in 5:5 states that “the years of your destruction (τὰ ἔτη τῆς ἀπωλείας ὑμῶν) will increase in an eternal curse (κατάρᾳ αἰώνων), and there will be no mercy or peace to you”. Here the destruction occurs not in a single moment but stretched over years spanning into eternity. It is a punishment that goes on forever because the evildoers would have no mercy or peace, which is exactly what they would receive if they are annihilated on the day of judgment.
(2) The fallen angels are bound “for seventy generations in the valleys of the earth, until the day of their judgment and consummation, until the eternal judgment is consummated. Then they will be led away to the fiery abyss and to the torture (τὸ χάος τοῦ πυρὸς καὶ εἰς τὴν βάσανον), and to the prison where they will be confined forever (τὸ δεσμωτήριον συνκλείσεως αἰῶνος)” (10:13). This is a clear reference to eternal torture of the fallen angels, and the next verse states that evildoers will share this same fate, “everyone who is condemned and destroyed henceforth will be bound together with them until the consummation of their generation” (v. 14). This suggests that there will be a final consummation, but not before a duration of fiery torment.
(3) In 1 Enoch 21-22, the visionary is given a tour of the great abyss and the mountain of the dead where the spirits of the dead are confined in deep hollows awaiting judgment. The abyss was “full of great pillars of fire (πλήρης στύλων πυρὸς μεγάλου) … a great fire burning and flaming there….This place is a prison (δεσμωτήριον) for the angels, here they will be confined forever (μέχρι αἰῶνος εἰς τὸν αἰῶνα)” (21:7-10) As for the evildoers, “here their spirits are separated for this great torment (τὴν μεγάλην βάσανον ταύτην), until the great day of judgment, of scourges and tortures of the cursed forever (τῶν μαστίγων καὶ τῶν βασάνων τῶν κατηραμένων μέχρι αἰῶνος), that there might be a recompense for their spirits. There he will bind them forever (ἐκεῖ δήσει αὐτοὺς μέχρις αἰῶνος.)” (22:11). Here the language is very plain. Evildoers will experience scourges and tortures forever; they will be bound in this prison forever. It is not a matter of being dead and nonexistent forever….it would be an existence of perpetual imprisonment and torture.
(4) A description of final judgment appears in the conclusion to the Animal Apocalypse: “And they went to the place of judgment, and they threw them into an abyss, and it was full of fire and it was burning and was full of pillars of fire. And those seventy shepherds [wicked angels] were judged and found to be sinners, and they were thrown into that fiery abyss. And I saw at that time that an abyss like it was opened in the middle of the earth, which was full of fire. And they brought those blinded sheep [evildoers] and they were all judged and found to be sinners. They were thrown into that fiery abyss, and they burned. And that abyss was to the south of that house” (90:24-27). This does not specify duration like the other passages but the idea here likewise is that the wicked share the same fate as the fallen angels. The geographical notice also indicates that the abyss in question is Gehenna.
(5) In 1 Enoch 100-103, the souls of the righteous come back to life and will not perish for all the generations of eternity (103:4) while the dead sinners are cursed and have no peace forever (100:3), “there will be in a great distress (ἐν ἀνάγκῃ μεγάλῃ), and in darkness and in a snare and in a flaming fire (ἐν παγίδι καὶ ἐν φλογὶ καιομένῃ). Into great judgment your souls will enter and the great judgment will be for all the generations of eternity (ἐν πάσαις ταῖς γενεαῖς τοῦ αἰῶνος); woe to you, you will have no peace (οὐκ ἔστιν ὑμῖν χαίρειν)” (103:7-8). This continues the same thought in 5:5, with the evildoers having no peace as they experience great distress in flaming fire for all generations of eternity. Annihilation in a single moment of destruction would to the contrary bring peace and an end to the distress.
A very similar picture can be found in the allusions to Gehenna in the synoptics, particularly Matthew. Mark 9:43-49 quotes Isaiah 66:24 and applies it to Gehenna, confirming that this OT passage lies behind references to Gehenna. This passage refers to the faithful worshiping at the Temple perpetually in an eschatological new earth (“from one New Moon to another and from one Sabbath to another”) as they watch the burning of their enemies in unquenchable fire nearby. The Markan passage includes the language of worms and unquenchable fire; the idea of Gehenna here is thus probably one that posits an enduring punishment (whether as sustained destruction or conscious torment) of the wicked that would be witnessed by those who enter into life. Matthew 18:8-9 redacts this Markan text, altering the reference to unquenchable fire to “eternal fire” and expanding “Gehenna” to “the Gehenna of fire”. Matthew also includes frequent references to conscious suffering (8:12, 13:42, 50, 22:13, 24:51, 25:30), indicating that he interpreted Isaiah 66:24 along similar lines as the author of Judith who wrote that the Lord “will take vengeance on them in the day of judgment, he will send fire and worms into their flesh, they shall weep in pain forever (κλαύσονται ἐν αἰσθήσει ἕως αἰῶνος)”. Sim also points to two other allusions to torture in Matthew.

The story of the demoniac in Mark 5:7 portrays the demons begging Jesus not to torture (βασανίσῃς) them by making them homeless through expulsion. But Matthew’s redaction of the story in 8:29 adds a new eschatological layer; the demons ask Jesus if he was coming to torture (βασανίσαι) them before the appointed time (πρὸ καιροῦ). The demons are concerned they would be tortured sooner than expected, alluding here to their final fate in 25:41 which is shared with the wicked. Moreover in the parable in Matthew 18:34, the master sends the unforgiving servant to the torturers (βασανισταῖς) to be tortured until he can pay off his debts. Jesus gives this an eschatological application: “This is how my heavenly Father will treat each of you unless you forgive your brother or sister from your heart” (v. 35). In other words, the wicked can expect God to hand them over to be tormented, which is the same fate that the demons fear (8:29, 25:41). The phrase ἕως οὗ ἀποδῷ πᾶν τὸ ὀφειλόμενον (expressing contingency that may or not be realized) also does not imply that debts will be paid. There is no guarantee that the imprisoned debtor has the means to pay every last penny to be able to get out of prison; he may be there for the rest of his life. The imprisonment and the tortures experienced are not what pays the debt and the fantastical debt of a hundred million denarii in Matthew 18:24 is meant to convey the sheer impossibility of repaying the debt, and thus the unending nature of the punishment.
Matthew portrays Gehenna as a place of habitation, characterized by torment. For Gehenna as an eschatological place, see ἐκεῖ in Matthew 8:12, 13:42, 50, 22:13, 24:51, 25:30. The accursed are sent to this place which had been prepared (ἑτοιμάζω) for the Devil and his demons; they all share the same fate. The verb ἑτοιμάζω here also occurs in v. 34 for the kingdom prepared for the righteous, and ἑτοιμάζω is similarly used in 20:23 to refer to the place where Jesus’ disciples would sit (καθίσαι) at his right hand. In view of this usage and the corresponding place where Jesus’ disciples would dwell, the natural reading is that Gehenna is also a place where the wicked, Satan, and the demons would dwell. Matthew 22:13 indicates that it is a prison, with the wicked bound (δήσαντες) hand and foot (πόδας καὶ χεῖρας) before they are cast (ἐκβάλετε) into the darkness (σκότος). The same imagery is found in 13:30 of the tares bound (δήσατε) to be burned. Matthew uses the verb δέω in reference to John the Baptist and Jesus imprisoned after their arrests (14:3, 27:2), and this verb is widely used in 1 Enoch to refer to the imprisonment of the fallen angels. In fact Matthew 22:13 agrees almost verbatim with 1 Enoch 10:4: “Go, Raphael, and bind (δήσον) Asael hand and foot (ποσὶν καὶ χερσίν) and cast (βάλε) him into the darkness (σκότος)”. So in light of the use of δέω in Matthew and the word’s apocalyptic context (compare Revelation 20:2), the language used of Gehenna is evocative of a place of confinement and carrying out a sentence or penalty as a consequence of judgment. This then brings us to the terminology of κόλασιν αἰώνιον in 25:46. With the imagery of confinement in view, κόλασις is best understood as punishment which has a lasting duration, and a punishment that involves tormentors (βασανισταῖς in 18:34).
Because of the dualist parallelism between εἰς κόλασιν αἰώνιον and εἰς ζωὴν αἰώνιον in 25:46 (note that the counterpart to eternal life is not eternal death but eternal punishment), the punishment would have an analogous duration (αἰώνιον) as the life enjoyed by the righteous (so if the punishment lasts only an “age”, so too would “eternal life” not be really eternal).
David Sim gives an extensive discussion of the gospel’s stance towards Jews and Gentiles (pp. 198-210), citing pro-Gentile statements in Matthew 2:1-12, 4:15-16, 8:5-13, 28-34, 12:18-19, 15:21-39, as well as anti-Gentile statements in 5:46-47, 6:7-8, 31-32, 18:15-17 (along with the depiction of the Gadarenes, Pontius Pilate, and the Roman executioners), which clarify the boundaries between Matthew’s community and other groups (the larger communities of formative institutional Judaism and the more numerous Gentiles who often had an acrimonious relationship with Jews in the wake of the war). He concludes that “Matthew’s anti-gentile sentiments, therefore, are directed at those who remain in the realm of the gentiles, just as his anti-Jewish statements are directed at those who reside in the world of formative Judaism. It is these gentiles, true gentiles from Matthew’s perspective, who are to be treated with suspicion and avoided. As to the number and status of the gentiles in the Matthean community, the evidence is not absolutely clear. A number of inferences, however, can be made on the basis of the existing evidence. It is almost certain that Jews comprised the greater part of the Matthean community and that gentile membership was comparatively small. The fact that this community perceived itself as a sect within formative Judaism and was involved in thoroughly Jewish issues is evidence enough of this.
Moreover, the probability that the Matthean community had only recently parted company with the synagogue also points in this direction…Although no longer within the synagogue, the members of Matthew’s church maintained unofficial contact with their Jewish opponents and were probably subjected to minor bouts of persecution as a result….The proposition that Matthew intends to stereotype all Jewish figures as wicked and all gentile characters as positive does not hold up to scrutiny on either count. It is based upon a very selective reading of the evidence and ignores the point that each group has a mixture of good and bad. The gentile world in Matthew’s gospel is thus not as open and friendly as is commonly thought. Just as Matthew specifies that Jesus was rejected and murdered by the Jews, so too does he specify that the gentiles were not innocent of either crime….Matt 10:18 refers to the missionaries being dragged before governors and kings to bear testimony before them and the gentiles. This verse bespeaks not only persecution at an official level by gentile officials, but also that they act with the assent of the whole gentile world….The mission discourse and the apocalyptic discourse, therefore, together indicate that Matthew’s view of the gentile world was not as positive as some scholars think. His community had suffered at the hands of the gentiles and was expecting to suffer even more as the eschatological timetable progressed according to divine plan. At the time the gospel was composed, this community perceived itself to be universally hated by the gentile nations” (pp. 198, 201, 204, 206-209).