Jellyfin can’t go closed source as it’s a fork of Emby from before it was closed source, licensed under the GPL. They don’t own that code so they can’t change that license, thus the whole project is GPL. In addition, Jellyfin isn’t being developed by just one company (it’s all volunteers), so every new contribution is also GPL licensed, owned by each contributor. The only way Jellyfin could go closed source would be to cut out the Emby backend and for every single contributor ever to agree to change the license, or have their code cut out. In short it’s not happening, and if somehow it did the project would just get forked regardless for everyone to switch to (the community did it once already!).

No, you have not understood anything. Assuming Jellyfin would go closed source, (ignoring the GPL license and so on) you would not notice anything. Your server and service would be unchanged by this.

Emby is the best example, the community will fork it and you server lives on. Even if not, then the server and software is still yours.