I don't think they'll be a middle-rate power though. I'd say they are a great power but not a hegemon. They basically control the eastern med and have either direct or indirect control of several of the most important sea lanes with the Bosporus, Suez Canal and the Strait of Malacca. That's a shitload of maritime traffic going through.
Right now they do, and they'll obvious hold the Bosphorus into the present day ITTL, though the Strait of Malacca and to some extent the Suez are more questionable. Decolonization didn't just happen out of the goodness of the western powers heart (lol), and while the Suez is geographically contiguous with the Roman core territory and much more important strategically for Rhomania than it was for Britain or France, Egypt is clearly going in the direction of developing its own identity distinct from the Anatolian heartlands much like with the OTL Ottoman Empire, and the intimation of growing discontent in Sicily for Constantinople's policies suggests that's also likely true with Roman Italy.
Without Egypt, Italy, (and this is mostly because the ERE looks hideous on a map with the Levant but not Egypt) the Levant, modern Rhomania could still be a globally relevant nation with a status similar to the "big three" of West/Central Europe (France, the UK, and Germany), which despite no longer being top powers remain major developed nations.
Haven't gotten AOM chills like this since the
Night of the Tocsins, can you believe it's over 2 years?!
Now that you mention that, it's rather striking that Rhomania's succession is
still the same old "whoever the army and the urban masses of Constantinople (in that order) says is Emperor" it's been since the days of classical Rome where primogeniture is only a tradition rather than inviolable law. In fact, I think the senate still technically proclaims the Emperor under the Roman constitution, though obviously that's never been more than a formality since classical Rome except during a brief stint during the Time of Troubles.
IIRC, at this point OTL royal succession in Latin Europe had become a highly formalized matter, and in ATL the western reaction to Demeterios being proclaimed Emperor suggests that to be the case ITTL as well.