Circus classes are awesome if you have any available near you, but keep an eye for out for calisthenics parks as well. They don’t tend to have formal classes associated with them, but it’s usually pretty easy to find a group of people that work out together at them. It’s like the bodyweight exercise version of a running club.
How about an obstacle course race like Tough Mudder or Spartan?
We have a trampoline gym in my city. I’ve been curious but chicken! 
If you want athleticism and superheroism on the same page as parkour and gymnastics, I’m seconding JcWoman’s climbing suggestion, specifically bouldering.
Ever watch American Ninja Warrior? Most of those guys are climbers, and they’re basically doing superhero style moves the whole show. Literally all of the most impressive superhero-ish people I know (including two who have been on the ANW show) are high-level climbers (specifically high level boulderers), and I’m a gym-rat who runs into a lot of fairly impressive people athletically.
I took up climbing around your age, so age isn’t really a barrier, and at least in the climbing gym, injuries are rare (be sure to always take any rings off though).
The group aspect is lacking in the sense there aren’t really any formal classes with 20 people, but there’s a ton of cameraderie and everyone is very helpful and friendly, and are almost universally happy to give pointers or tips or answer questions you might have about how they just did something difficult.