Currently basegame great people give influence like this:

Great Writer, Great Artist, Great Musician: Cultured
Great Scientist, Great Admiral: Maritime
Great General: Militaristic
Great Merchant, Great Engineer: Mercantile
Great Prophet: Religious

More information is available on the wiki

Continuing from previous post:

Also, do Great Engineers and Scientists not provide any bonuses? There are 5 CS types and 9 GP types, so perhaps they could be regrouped more evenly? E.g Engineers+Generals boosting Militaristic, Writers+Merchants boosting Mercantile, etc. Or the other way around, e.g. Generals boosting Militaristic+Cultured, Engineers boosting Militaristic+Religious, etc.

Or perhaps, Engineers and Scientists could give a different boost, maybe in the same sense as my first suggestion? E.g. they could both give +1 to all aside from Cultured, while Engineers could increase the defense of the city and allied CSs and Scientists could act as counter-spies for friendly CSs?

Regardless, as I've said it looks fun as is, I just wanted to give these suggestions since I think they'd make things more fun, while not deviating from your proposal of mostly only affecting CSs.

Agreed, it sounds both fitting and fun to play as. Looking forward to it. I'd like to bring up some suggestions, though, which I'll have to split due to character limit:

Since there are 3 cultured Great People, how about differentiating them? E.g. instead of all giving +2 to Cultured CSs, how about making them all give +1 but each has a unique effect for all city states? I haven't given this too much thought, but Writers could lower the threshold for demanding tribute and/or the influence loss for doing so, Musicians could reduce the natural influence deterioration, and Artists could give give an influence boost to all CSs whenever you gift gold to one?

Very fitting and fun concept, stellar work!

Another one of the factions from the Nobunaga's Ambition: Taishi.