The Python Software Foundation acts as a fiscal sponsor for a much smaller set of orgs (20 listed on https://www.python.org/psf/fiscal-sponsorees/) and it keeps our accounting team pretty busy just looking after those. Hack Club must have this down to a very fine art.
I wrote a bit more about PSF fiscal sponsorship here: https://simonwillison.net/2024/Sep/18/board-of-the-python-so...
I was working with Hack Club students on an experimental VPN client (https://github.com/hackclub/burrow) but never got the momentum to finish it. Made some great friends, though! It's a really fantastic organization.
The students have one big global Slack instance. If you're a student and on here, you should also be in there: https://hackclub.com/slack/
The “understanding through building” mentality is something I never got to experience as a group, the obvious answer is open source and the like but I wonder if there’s something more learning oriented.
In any case, good luck on finding the right community!