And have you ever gotten a GS or GE from the patronage finisher? I don't think any CSs are coded to provide those.
I'm all but positive that I have gotten GSs from city states more than once, but when you ask like that, you do give me an inchling of doubt. I thought it was random which great person you got so never paid attention to which kind of city state offered me what. Is there anything in the source code which gives us information about what kind of great persons that should be linked to certain city state types?
As for the OP, I like to go Piety for second tree, but then I play with moderately modded policy trees, so I don't quite follow the paths of other players - I start with Liberty as often as Tradition (if not more, since I generally like playing wide), and I only occasionally take full Rationalism. Piety is good when playing wide because it helps you get religious buildings in larger numbers and the extra faith is also useful for GP purchase later in game. Plus if I forgo Tradition and/or Rationalism the reformation belief "To The Glory Of God" is a fantastic benefit (and AI never takes this belief, unlike Jesuit Education and Sacred Sites which is all but always gone by the time I get to Reformation if I go full Piety.
Opening Patronage and taking 1-2 policies in this tree is generally always worth it for me. Forbidden Palace is one of the best wonders imo. (again even more so if going wide) plus as others have said, city state allies never hurt.
If many cities are coastal, opening Exploration for the production bonus in coastal cities also can be worth it. Exploration opener isn't too great however, and the lower tree is also pretty awful in unmodded game, so finishing Exploration is generally only worth it for the hidden antiquity sites, which basically means paying for culture with culture.
Opening Commerce is generally not the most valuable choice imo. but on the other hand, more gold never hurts, so if you find yourself in a situation where you don't have any obvious picks, I think that's a safe filler. It's definitely better than Aesthetics opener and top tree which is downright awful imo., only reason I would ever go into Aesthetics is if I plan cultural victory and then I need to rush it.