I remember the devs telling us that when the game is released, there would be information about how each civic is triggered. I can't seem to find this anywhere on the UI or the game's encyclopedia.

Wiki seems to have information on some of them, possibly through experimentation.

https://humankind.fandom.com/wiki/Civic

Specifically, I really want to know about "leadership", so I can get 3 city faster.

Sorry, it's still pretty opaque. I've been playing nearly non-stop since release and couldn't tell you the exact conditions.

I guess its my playstyle but I have never triggered the civics that require 3 common and 3 financial districts in a city.

That's a start : https://humankind.fandom.com/wiki/Civic