> All the texts that mention the Hittites post-date the fall of the empire based out of Ḫattuša by centuries

I don't see how this would invalidate the legitimacy of the documentation. The Hittites were large enough to be visible to contemporary historians and scriptures were used for information preserval. Even if our knowledge was only preserved through written documents, we'd have a good grasp of history 300 years ago, especially of major societies. People weren't primitive back then, they even had state archives with historical records which the Bible mentions in a few places for further reading.

We're talking about a Levantine Iron Age text discussing Bronze Age peoples where civilization collapsed in the interim. In the case of Ḫattuša, the state archives were almost certainly unreadable by the time the Biblical texts were written, evidenced by the lack of any Hittite cuneiform texts being produced or copied in the Iron Age. Egypt and Mesopotamia maintained texts and the ability to read those texts across the collapse. The same cannot be said about Syria-Anatolia and the Levant.

That isn't to say that the Biblical texts can't reflect a memory passed on through oral tradition or knowledge from Mesopotamia and Egypt. But given that the geography of the Hittites of the Bible seems to line up more with the later "Neo-Hittite" Luwian-Arameans than Ḫattuša and that the Bible doesn't seem to be aware of the empire of Ḫattuša, the Biblical Hittites are probably not Ḫattuša.