I just can’t see a technologically advanced civilization reverting to barbarism in 120 years just because they couldn’t use warp drive anymore. It makes zero sense to me.
There were the temporal wars about a hundred years before the arrival of the Discovery and as we have heard and seen in "Unification III", there was already a lot of trouble brewing for the Federation because of the dilitium shortage even before the burn. It's very possible imho and even hinted at that the Federation already had a lot of internal problems to deal with, even before the calamity.
When the burn happened it may have caused wars on some already instable worlds that could have left some worlds in a state where they lost a lot of their scientific knowledge with only some myths about a former golden age remaining behind.
Actually maybe a bit like Earth was shown to be like, around the same time, in Babylon 5's "Deconstruction of Falling Stars", where the war that caused it was also called the "burn"