technology

I truly do not understand how to work with Bazzite's immutable file structure.

Yep it's good until it isn't imo, it's good for casual users but once you try something with it, it's a PITA, I personally use CachyOS. Containerizing the media server, in this case, is better insofar they can push an update to the image and instantly update it and all dependencies, it's a "clean" slate and the program isn't spread through your filesystem everywhere, it's configured directly through the yaml file, and it's replicable so if you send them a bug report they will know you run X version which wont have build differences; though containerization has a small overhead, though if the image is good, it's largely reliable (I use containers on production servers). Tbh introducing your average Desktop user to running docker/podman containers seems like not a good idea on their part, especially for Desktop apps, I get the dev point though, but it's in tune with the whole immutability of the systems, while a neat idea for many they personally annoy me

With Plex you'd do something like:

# ~/.config/containers/systemd/plex.container
[Container]
ContainerName=plex
Environment=TZ=Your/TimeZone
Environment=PLEX_CLAIM="<claimToken>"
Image=docker.io/plexinc/pms-docker
AutoUpdate=registry
Network=host
Volume=/home/user/.config/plex:/config:z
Volume=/home/user/.cache/plex-transcode:/transcode:z
Volume=/home/user/Movies:/data:z

# Remove if you don't want autostart
[Install]
WantedBy=default.target

Then execute:

systemctl daemon-reload

# Autostart Plex at boot, if you want
systemctl enable plex.service 

systemctl start plex.service

Though FYI I've never used Plex, this is mostly me doing it mentally, If you need a good resource there is https://wiki.archlinux.org/title/Podman#Quadlet though it's dense and informative as usually the ArchWiki is. Let me know if you have any issues