The idea of a ‘Bronze Age’ or a ‘Bronze Age collapse’ was never any kind of folk idea. As a period, as a categorisation, the ‘Bronze Age’ is entirely a modern construct; the ‘collapse’ is entirely a finding of modern archaeology.

The idea of a Bronze Age was first formulated in the 1820s-1830s by the Danish antiquarian Christian Jürgensen Thomsen, who realised that there was a correlation between the date of prehistoric artefacts and typical materials out of which they were made. He accordingly coined the terms ‘Stone Age’, ‘Bronze Age’, and ‘Iron Age’.

The idea of a collapse is more recent, but it’s critical to convey that it doesn’t refer to a collapse of every Bronze Age civilisation everywhere in the world, or even a universal collapse in one region of the world. It refers to the collapse of two specific cultures: the Hittite empire, including a number of Hittite-aligned cities in Anatolia and the Levant; and the Mycenaean palace culture in Greece.
The ‘Bronze Age collapse’ ended two significant ancient Mediterranean cultures, but it didn’t affect everyone. The Egyptian New Kingdom hummed along for a century afterwards; the Assyrians were barely affected. Even Hittite and Greek cultures had certain forms of continuity following the collapse.
To add to this, although the Hittite empire splintered into smaller kingdoms toward the end of the Bronze Age (I touched on this in How did the civilizations fall in the end of the Bronze Age?), many aspects of Hittite civilization survived in southern Anatolia and Syria – religious beliefs and practices, Luwian and the Anatolian hieroglyphic writing system, architectural and artistic styles, administrative titles, Hittite royal names (e.g. Šuppiluliuma and Ḫattušili), and so on. Carchemish and Malatya in particular had royal lines descended from the Hittite Great Kings of the Bronze Age that continued unbroken into the Iron Age. Additionally, the construction and decoration of palaces and monumental buildings continued in the Early Iron Age, such as the reliefs and inscriptions of the temple of the Storm God at Aleppo (11th century BCE). These Syro-Anatolian kingdoms were still referred to as “Hittite” by their neighbors like the Assyrians as late as the 7th century BCE.

As the Hittitologist Gary Beckman put it in “From Hattusa to Carchemish: The Latest on Hittite History,”
The Hittite empire was always a fragile structure, tending to disintegration whenever the power of Ḫattuša weakened. What is most remarkable is just how long this polity resisted the centrifugal forces affecting it. In newly accessible sources we may see how a prolonged civil war between the descendants of Ḫattušili III in Ḫattuša and the line of Muwattalli II reigning in the southern Anatolian city of Tarḫuntašša exacerbated this situation and contributed to the ultimate demise of Ḫatti. Recent excavations at Boğazköy have shown that the capital was not destroyed in a single conflagration, but was gradually abandoned over the course of the early decades of the twelfth century. This suggests that the fall of the Hittites was not a cataclysmic event, as often portrayed, but rather a process in which peripheral areas responded to division and debility at the center by breaking away, leading to a progressive decline in the wealth and military might available to the capital and its rulers. After a certain point, recovery would have become impossible.

Indeed, the outlines of the transition to the political constellation of the early Iron Age in Anatolia and northern Syria are beginning to emerge, and for Ḫatti we may discern fragmentation rather than destruction… While the dominion of Ḫattuša vanished forever, the kings of Tarḫuntašša (Kurunta-Mursili-Hartappu) maintained their positions well into the twelfth century, and the cadet line established by Šuppiluliuma I at Carchemish as Hittite viceroys in Syria continued uninterrupted into the “Neo-Hittite” period.