well I think orthodox caucasians (well trebizond included) have a much harder time than the shia guys because the shia guys don't face existential threats most of the time
That's true if you just want to sit there and rot, but to be fair you can do that as Georgia becoming QQ's vassal, too. It's not like they'll annex you before behing shanked by the Ottomans or someone else and imploding.
Gazi and Shirvan are more poor, have a weaker starting army, and a weaker tech group that can't later on click button insta-westernize, and similar to the Orthodox nations expansion options before everything is wrong-religion are limited.
I mean, you can probably just take Bosnia, ally Hungary or Poland and sit there as Serbia, too. But winning as Gazi or Shirvan means using very limited alliance options to defeat nations that are stronger than you are. Easier than Trebizond? Sure. Easier than BYZ though? Not so much.