okay so im just going to picture this Byzantium as holding onto western Anatolia during the 13th-14th centuries as well as Greece with maybe some gradual reclamation of territory on the northern part of Anatolia, as it pushes raiders out with superior gunpowder weaponry around the 17th-18th century (analogous to Russia gaining the upper hand and and going after the khanates). This gives them an amount of arable land 3-4 times that of modern day Greece.
Couple this with having a relatively prosperous Constantinople and having good control of the straits, (as well as hopefully weakening or ridding the state of Italian influence) this could lead to a country roughly equal in terms of wealth to England during the 16th century. So no world power but definitely a regional one as far as i can tell.
However we should note that this area was traditionally on the edge of great mongol and Timurid Invasions and so could be periodically wrecked by those until gunpowder reigns supreme.