Whether, as
@acluewithout asserts and you may also be suggesting with your first paragraph, it also affects their behaviour in other ways, that's the part I'm sceptical about, but would like to see implemented if it isn't currently a thing.
According to the wiki, only certain leaders have an agenda that would directly affect their behavior:
-Catherine likes to build spies
-Seondeok focuses on science output
-Amanitore maximizes district count per city
-Robert will abstain from war declarations except for broken promises (but presumably will be dragged into alliance wars)
-Shaka will maximize corps and armies
-Ghengis Khan will focus on cavalry
-Poundmaker tries to make as many alliances as his relationship score will allow (this may not actually have a discernible effect since the AI is bad at making friends with each other)
-Frederick conquers city states (is there anyone who doesn’t?)(I think Robert and Tamar might actually avoid CS conquering, but they don’t try to liberate that I’ve seen)
-Harold builds boats
-Tamar builds walls
-Cyrus declares surprise wars
-Ghandi doesn’t declare war
-Cleopatra tries to make alliances with militarily strong civs (unclear how)
-Jadwiga builds faith buildings
-Lautaro tries to keep high loyalty (unclear when this would be an issue that others wouldn’t also try to resolve)
-Victoria expands to every continent
-Montezuma collects luxuries (unclear how)
-Qi Shi Huang builds wonders
-Gorgo never gives anything for peace (I can confirm this one)
-Pedro tries to get great people
-Saladin builds worship buildings (I think that refers to the T3 buildings)
The other ~14 leaders have essentially no behavior that could be observed by the player in their set agenda. The hidden agendas could also affect direct actions though.
Regardless, these are all direct actions that we should be looking for if we’re tying to determine if there’s a difference in the behavior trees. Many of these are things I can at least anecdotally confirm. However, some of them only would be triggered in rare situations, or the resulting action is basically undiscriminably different than default behavior.