I’ve been using Fedora CoreOS as my main server in my home lab for a couple years now and have been very happy with it. You still get the convenience of automatic atomic updates and you also have the flexibility of being able to install whatever additional Fedora packages you need with rpm-ostree.
I installed Docker Engine and docker-compose from upstream. You should be able to set SELinux to permissive mode if you need to so it doesn’t enforce any policies.
Search for portable Jellyfin media server projects. It looks like there’s a few out there.
If you’re going to use this in a car, it needs to be as simple as plugging in a single device and powering it on. An over-engineered solution is going to quickly turn into a headache.