I picture the modern Roman Empire being in the great power category. Whilst not having the population or material resources of some of the really big powers (think alt USA or Russia) they would have a lead in administration, organization and technical efficiency. A good example might be a nation with France or Austria-Hungary level of population and material resources, but with Germany’s organization and Britain’s financial acumen.
That seems about right, going by the 1625 map even the portions directly controlled by Constantinople would give them a modern population of ~150 million just by today's numbers and they can likely get much higher, probably between 180 - 200 million. If they can incorporate all the vassals you are looking at an easy 250 million people with just the core Mediterranean areas. Depending on what portions of the colonial territories enter the core empire you could likely have a population that is in the top five even today as shown below.
Resources is where it gets tricky but they are not exactly poor, not like Japan or Germany, and since there is unlikely to be an ATL USA that takes over North America that leaves whatever Russia forms and China as the resource giants but good relations with the Americas and Africa could go a long way to ameliorate that issue which would put the Roman empire at the top of the great power spectrum but well short of super power, at the moment only China has that potential in the TL.
World Population 2018
1
China 1,415,045,928
2
India 1,354,051,854
Roman Empire with vassals and colonies incorporated ~300,000,000 - 500,000,000: this one really depends on how much of the south east Asia, especially the OTL Philippines, they get/keep.
3
U.S. 326,766,748
4
Indonesia 266,794,980
Roman Empire with all vassals, especially Egypt, incorporated ~250,000,000
5
Brazil 210,867,954
6
Pakistan 200,813,818
7
Nigeria 195,875,237
8
Bangladesh 166,368,149
Roman Empire with current borders ~150,000,000
9
Russia 143,964,709
10
Mexico 130,759,074
