I find the real reason the Ottomans underperform is that their provinces are too poor. EU3 favors the west the most when it comes to tax and manpower. Historical population is worth more manpower per person in the game the farther towards France you move (which is why France has a much bigger manpower pool than all of India combined). Taxbase is more abstract, but I'd say the same trend is evident there.
While it's certainly true that EU favours Europe, I don't think that's the main issue here. I did an analysis and Anatolia is not particularly too poor compared to, say, France. (It's not perfect, but compared to the problems with India, China, Viet Nam, etc. etc., and allowing for the fact that ratios of population between countries could change significantly over 4 centuries but they don't in game, it's a decent approximation.)
There are four areas in Europe that are substantially overpowered even compared to the rest of Europe: Sweden, Austria, Super-Aquileia

(I have no idea why Cortes went all the way to Mexico when Aquileia had just as much gold as the Aztecs), and Greece. Historically, the population of Anatolia outnumbered that of Greece by a factor of something on the order of 4:1 or 6:1 during this period. In EU3, before 1453 the Greek provinces have the same tax base as the Turkish ones. Even after Constantinople gets reclassified as Turkish the Turks only have a 4:3 margin. Again, this is because the Greeks are far too numerous, not because the Turks are especially badly represented. So yes,
of course if the resources of the Greek peninsula had been 5x what they historically were, Byzantium would have stood a much better chance of surviving the early 1400's. And of course the Turks would have had more issues controlling Greece if there had been as many Greeks as Turks.
Another problem the Turks have that's new to Divine Wind is that the Golden Horde hates them with an undying hatred, whereas historically the Ottomans and the Crimean Horde were allies and partners. In earlier versions of EU3 the Hordes of Russia were usually allied to the Ottomans. This is a very major deterioration in the Ottomans' strategic position.
The comeback that they did not made historically, and that would be making it basically that much harder for the player? Oh noes! I agree, for gods sake, give the ottomans a non-blockable strait there. And make it, that most european nations stop eating north africa. It´s dirt poor as it is, so it really shouldn´t be so big a target for the AI.
Sure.
Keep the unrealistic population and resources the Greeks have.
Keep all the arbitrary cores the Byzantines have on lands they hadn't controlled since Manzikert.
Keep 1399 Thrace valued as if it's the capital of a major power, rather than starting it poor and increasing its value after 1453.
But remove a realistic feature: the fact that the Straits can be blocked by naval power. The Straits were blocked by naval power to considerable historic effect on a couple of significant occasions in the first millenium, and it's absolutely realistic for the 1453 Turks' naval power to be competent to prevent the Byzantines from crossing the Strait with an army.
It is kinda weird that Castille has no problems crossing the Mediterranean but the Ottomans can't cross a darn strait. Was a blockable strait such a problem in EU2? Was it a similar situation? It's been years since I could find my well-played EU2 disc.
If the Ottomans and the Byzantines had historically accurate resources, the absolute naval dominance of the Strait by the Ottomans would not be in any question.
To answer your original question:
The game effects of being in the same tech group include sharing technological development (through neighbour bonuses), units, and maps. Therefore, it's good that the Ottomans got moved into a different tech group from the Russians, as historically the Ottomans and the Russians did not go out of their way to help each other technologically, they had distinct unit types (it's bad for flavour if someone playing the Russians has units named things like "Janissaries"), and they interacted with different sets of countries: Russia shouldn't have diplomatic relations with Ethiopia, but the Ottomans should.
It also makes sense for the Ottomans should have a unique unit tree, and IIRC the way the .exe is, to define a unit tree you have to define a tech group of that name first.
What does not make sense is that the Ottomans do not share technological development with other Muslim countries. Of course they did!
So IMO the Ottomans (and the other "Ottoman" tech group countries) should be part of the Muslim tech group, but the Ottomans should have their own customized unit type and maybe a 10% tech bonus or tech cost discount from a modifier.