Sakuramoria

I still don't understand, are the clubs meant to be purely role-playing, or can they have their own unique mechanics?

Whatever you want, that's what they'll be.
The ones mentioned are just examples. If you just need role-playing clubs, and not ones with mechanics, then that's fine too. Just remember, they need to be either suggested by Revana (or some other NPCs), or come up with them yourselves, as students who are interested in this.
And 99% of the micromanagement should be left out of the game, either on Levizia, or with the club leaders (either you or NPCs).