As best I recall western (latin) historiography ITTL more or less states the “Roman” empire fell with the sack of Constantinople in 1204. The current “Roman” empire is simply the Greek Empire in Western Europe that grew from Nicea. It has barely more claim to be “Roman” than say Arles or Spain. It may occupy traditionally Roman areas but it isn’t Roman merely a very successful successor state.Yeah, something along the lines of "Those Greeks used to be the heirs to the great and glorious Western traditions, a damn shame they fell somewhere along the way and now us True Roman Descendants are the real movers and shakers."
I'm sure somewhere in the archives is a Western ambassador or general or philospher expousing such rhetoric ITTL. Maybe later today I'll try and wade through the posts and see if I can find one.
To further the break with Rome western historiography emphasizes the large Turkish and Armenian components of the empire to make the claim that although Rhomania may occupy European lands it is fundamentally an Eastern power with European characteristics rather than a European power with Eastern characteristics.
The fact that the current dynasty is a mix of Greek, Turkish. Ethiopian, and Steppe Nomad with I am sure a very “dusky” appearance and that the only other state with a “Roman” emperor is Persia of all places would also be strongly used to imply that Rhomania isn’t Rome regardless of its name or the territory it occupies. Now for diplomatic purposes Rhomania is likely given the title de facto in terms of prestige but it is not at all emphasized outside of that. (By diplomatic I mean the Roman ambassador would be ushered into a meeting before the Triune, HRE, or Kalmar emperor as the title of Roman Emperor is older than all of them and thus gets preference)
Ironically it is likely the Muslim world rather than Europe that probably recognizes Rhomania as the Roman Empire in fact as well as diplomatic niceties. For the Muslim world this is fundamentally the same state that has been fought for a millennia now. The fact that it temporarily lost its capital is immaterial as even during that time Nicea reconquered Muslim lands in Anatolia.
Anyways that’s as best I can recall as I think a similar discussion was had about this 2 or 3 years ago.