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.

You're right that we don't have a full story of why it happened, and you're right that the central evidence for a 'collapse' is archaeological. Prior to the 1100s BCE, we have evidence of wealth, bureaucracy, and large-scale political structures in the Hittite and Mycenaean worlds; afterwards, we don't. That's what the 'collapse' refers to. All this evidence was a modern discovery.

So when you mention 'an imaginary folk idea', and 'public memory of sorts', I have a sneaking suspicion that you've been reading some things with a strongly euhemeristic leaning. Euhemerism refers to the notion that myths and legends contain historical kernels. In certain trivial senses that's true -- myths contain real natural and human phenomena, like weather, politics, sexuality, war, etc. -- but the idea that myths are based on specific historical events is usually baseless, and where it does work, it relies on cherry-picking.

There are no myths about the fall of the Hittite empire. There's no 'folk idea' about it, no memory. There continued to be Hittites in certain regions of the former empire, but the empire itself was completely forgotten.

In the Greek world, some modern people have sometimes interpreted some Greek legends as referring to 12th century BCE events: that idea is taken seriously in some circles, even by some scholars in academia, but it's always very very selective.

Even if we do take the idea seriously, still, the legends that we have are always coded with ideas belonging to the time when the legends appeared, dating to the 7th century or later, not belonging to the time of the Bronze Age collapse. Homer's Troy, for example, has a civic cult of Ilian Athena in Iliad 6 -- a cult that didn't exist until around 700 BCE.

The idea that reality is represented in some later legends is basically just pattern-hunting. It only works because it's selective. It's easy to cherry-pick parallels between later legends and the collapse of some centres -- well, I say 'some': really it's just one centre, Troy.

The parallels dry up very quickly if you look elsewhere and treat the evidence impartially. Greek myth has it that Troy was completely destroyed; in reality, Troy was inhabited continuously until around 950 BCE. Conversely, places like Mycenae, Tiryns, Gla, Pylos, Hattusa, and Ugarit were completely destroyed -- but there are no myths about them.

To sum up: the Bronze Age collapse is strictly a modern archaeological discovery, not something known from any ancient folk tradition.