The Candarids or Germiyanids become the Byzantine Empire's principle threat. The former are mostly a bog standard steppe confederation, the latter are the real threat given they were much more organized than the other beyliks. I don't think the Byzantines are doomed per se, so long as their civil wars are avoided and their energies are focused on crushing threats abroad. You've got just enough time to butterfly Andronikos II's long, disastrous reign. Do that and the empire's in a much better place.
However given you just butterflied away the migration if the Ottoman clan into western Anatolia in the late 1200s, you change quite a lot of the power politics in Anatolia and Rhomania. Lots of different ways this could go about. Kinda hard to tell because of that actually, other than pointing at who becomes the top dog amongst the Western Beyliks. They were more likely to fight each other as they were the Greeks.