I can try and tackle this from a Western perspective! By Late Antiquity, these regions were very Romanized, to the point that the people that were left behind following the collapse of Rome would have, for the most part, identified as Romans - we must bear in mind that the last significant territorial expansion by the Romans was in the second century, almost three hundred years prior to the collapse of the empire; so most people living within the empire had been doing so for countless generations by this point (at least this was the case in the West, I won't speak to Eastern Regions too much, although they mostly remain as Romani/Ρομανοι). As such, the reversion to 'native' culture actually becomes a push for the 'revival' of Roman culture, in some cases, under their new Germanic leaders. For the most part, this is happening with the result that these new kings, who themselves were the leaders of warring bands of individuals which had since claimed ownership over these lands, could effectively maintain power over a vast array of different social and cultural backgrounds. So in a way, many Germanic leaders took it upon themselves to undergo some extent of Romanization so as not to upset the cultural status quo of the regions that they've taken control over. This is sometimes described as the leader's maintaining an 'equidistance' over the various peoples they ruled over.

I think the best example of this is certainly in Italy, with the Ostrogothic leader Theoderic the Amal. Theoderic's capture of Italy was a peaceful one (as far as these things go), with him deposing Odoacer as king. Once he took the mantle for himself, we see him pushing forward with a number of policies which can be seen as pro-Roman, such as maintaining Roman education (with some of his own family, Theodohad and Amalasuentha, receiving Roman education). Similrly, the government remained fairly similar, with him holding great respect for the Roman senate, as well as maintaining the curial system in the cities he oversaw. It is generally the case that the traditional Roman worldview and culture was maintained under Theoderic, but it wasn't only because of his maintaining of the late antique status quo. He also had a fairly extensive cultural program, one strand of which being a building program where he sought to 'restore' Rome via architecture.

Theoderic's leadership style as the 'builder' really demonstrates how he was particularly interested in restoring Romanness with what is now referred to as a renovatio urbium (the restoration of the cities). We can see this play out in the Variae of Cassiodorus, essentially a collection of letters and decrees from Theoderic's rule, where architecture features quite heavily. We even get sections which provide us with the motivation behind these building programs, such as this section 2.39.1 (from Shane Bjornlie's translation, regarding the restoration of a bath house at Aponus):

If we want to join the wonders heard of the ancients to praise for our clemency, with nothing diminished under our care, since fame is the prosperity of a king, with what zeal should that which often happens to come before our eyes seem fit to be restored? Indeed, it is a delight to recall the efficacy of health-bearing Aponus. For this reason, as you know, we desire to make new what has not been able escape our memory.

With this quotation, we're given the motivation of this renovation as being directly linked with antiquarianism (that is, the restoration of antiquity, or in this case, the restoration of Roman culture). His building program would ultimately be a combination of restoration projects, such as this example at Aponus, paired with new constructions (habitations, workshops) which helped in the general restoration of older sites and areas.

So we can see that through this example of Theoderic's building program, he was interested in a general push in antiquarianizing his kingdom, both to blend his new Gothic culture back into the Roman culture which he was effectively invading, but perhaps also to lend some legitimacy to his leadership (through the badge of antiquity). But something also to bear in mind is that when speaking in terms of culture, to break things down into designations such as 'Roman', 'Ostrogothic', 'Frankish' etc is to prescribe a bit to ethnogenesis theories, which somewhat rely on the whole colonial mindset of systemically categorizing cultures when in fact the reality may have been far more diverse or complex - so a discussion on cultures in this period should also always be taken with a grain of salt, which is why I'm purposefully focusing on the intent of a single leader, and not what the general feelings were towards culture in this period. In fact, it's still hard to narrow down how the Goths and Italo-Romans merged, with some accounts suggesting inter-marrying between the two groups, while some suggest that the Goths tended to settle mostly in the North, in military-esque settlements (this plays into the idea that Theoderic began to identify the military as 'Gothic' and the civic body as 'Roman', although certainly individuals of either side crossed between these lines). Despite these complications, we can still come to the end of a thread here that Theoderic wanted to integrate into the culture which existed in the region prior to him, and architecture was just one strand of this program.