Plex Inc has a central auth server, and your media server automatically creates a dynamic hostname for connecting to your server’s IP. And if the user can’t reach the server directly for some reason (NAT for example), Plex has a “relay server” that works as a proxy, but your quality gets reduced to like 320p or something.
So if Plex Inc shut down their auth servers suddenly (or have downtime, which happened a couple years ago), you won’t be able to do much. It’s possible to bypass the central auth, but no one does it, because such auto-discovery is one of Plex’s benefits – user logs in on their app, and it shows all their possible servers. But otherwise, it’s self-hosted.
Unless you have somehow managed to get the source code, no, Plex is not free software unfortunately!