

Teamspeak still requires a license above a small user size, but has multiple clients that can accomodate different target audicences. The TS3 client still looks like it did back in the windows 7 days and the TS5 client is just copying discords homework (Not a clue what happend to 4 and I believe 6 is under development). Both use the same server backend and database structure so both work with one server and different user expirences.
Mumble is still the gold standard for handling large user bases (there is a reason big EvE Online alliances use mumble). It will take longer to set up, the configuration is handled by the server, not through authorized user accounts like TS.
Its pretty similar to Lemmy or anything else in the fediverse, someones full user name includes their home server.
Your admin just needs to have configured the service to except comminication from other servers and not just its internal users.