course Byzantium with a strong Komnenian state could develop ala its western European counterparts hell I could even see it being a power by 19th century provided it controls Anatolia and the balkans be of equal to Britain.
The reason is simple even in Manuel's reign Byzantine gdp per capita was around 1100 international dollars. It also had a high literacy rate of over 30%. These numbers would not be surpassed by any European nations till 1700s by which point Britain achieves 40% literacy and once industrialization takes off surpasses byzantine gdp per capita figure. It takes much longer for France to beat those numbers and even longer in the case of Ottomans or Russians or even Austria-Hungary. That coupled with its
trading
and manufacturing based economy and even some coal fields in northern anatolia+deforestation, it will be in a very good position to industrialize since the majority of requirements are already met.
The key difference beetween the Ottoman state and a byzantium that replaces it is that the Ottomans were a state based on agriculture. They were not a manufacturing based empire. Byzantium was since its dominance over Manufacturing in the med and its
trade
powers were vital to its survival as a nation. At the same time wages in ottoman lands were low but Byzantine workers usually were paid high wages due toe enjoying higher standard of living at least in peaceful times then their western european counterparts. Due to this key difference I see the byzantine state developing gunpowder roughly the same time as other european states and in fact be one of the premier european powers if we get a successful Komnenian restoration. The big issues it will face however are the landholding dynatoi. Though europe also had feudalism so perhaps Byzantium can develop into a more centralized state.
As for its threats. Well the big one would be perhaps Austria(if like otl they become HRE), the Italian city states, especially Venice though im certain by 1800s due to industrialization and high agricultural productivity byzantium will essentially win out. Also Spain in the med. I could see it allying with France like otl Ottomans and Italy could be the main battleground in any big conflicts it takes part in. perhaps Russia would be an ally if it does form since both are Orthodox and
share
many ties.
Thus by 1900 I expect Byzantium to be one of the great powers. In terms of economic and manufacturing potential somewhere between France and Britain/Germany. though in terms of standing armies it would be more on pairity with otl France.
As for population otl the turks in anatolia were still very nomadic even by the late 1800s I beleive and due to lack of agricultural productivity in land ottoman populations were low. The Romans I doubt would face similar issues and in otl before Turkish conquest Anatolia was heavily populated. Not to mention as a european nation technological diffusons from Netherlands would also reach byzantium.
All this assumes that a stronger byzantium retains its reliance on trade and manuacturing.