Jam is open source so you can look at the code but also make changes if you want to (e.g. if you prefer different reaction emoji). While not trivial it definitely is a great option to have imho.
Last but not least we designed Jam in a way that works well stand-alone but also makes it easy to integrate in existing web and mobile apps. For example there are people who run forums/communities or saas b2b apps (e.g. productivity tools) who want to add audio rooms as a feature and with Jam they can just grab the code and add rooms using an iframe (or use the JavaScript library for more advanced integrations). Not sure if that's possible with teamspeak, ventrilo or discord?
Jam is p2p WebRTC w/ low-latency and high-quality audio (opus) so it _should_ work well for competitive gaming. If you are looking for an audio chat tool designed for gaming the existing solutions you mentioned might be a better fit but happy to learn more about how we could make Jam better there as well.
I'd like to try a server with it and test a bit, but wonder if I self hosted, could I tell the software to use a TURN server only and block the p2p?
( For my use cases I need to prevent people from getting easy access to other people's ip addys )
Instead, how is it better than Jitsi and Mumble, given that they are already well tested and widespread?
That said: if you are looking for something that has room concepts close to Clubhouse or Twitter Spaces (you see who is in the room, who is speaking, you can move people between audience and stage and so on) and an easy way to add those rooms to existing (web) or mobile apps then Jam is great out of the box. If you are looking for screen sharing or video then Jitsi is a better starting point right now I think.
Mumble I am not very familiar with but it looks interesting. As far as I understand it is not web based but like Jam it also is p2p and uses opus for audio (low latency, high quality)? Perhaps someone who knows Mumble can do a comparison.
Your use of Opus and the option to run a SFU makes this a suitable replacement of Mumble for meetings, like in the Pirate Parties around the world. We are heavy users of Mumble.