Already moved my community to Matrix/Element last year. Haven't looked back.
uxellodunum
I'm assuming you're just running bare-metal, in which case no GPU passthrough would be needed. From what you've mentioned, everything seems about right so not much more to say - But on the UI department I do agree most apps could use some polish. I'd really recommend you try to replicate, get the logs, and forward them either to the Jellyfin Forums or their troubleshooting Matrix room (or both!), as people are generally quite helpful. Best of luck!
Nice to see Matrix's Element client on there. Has definitely become my go-to and even managed to get friends, family, and my gaming community on there, replacing Discord entirely
Don't get the EU flag though, we should be pushing for global sovereign alternatives. Thos could indicate the inverse in that these applications/platforms are not useable outside EU which is incorrect, and unfortunate.
You mention about 3 different issues, but files not playing is definitely a config/file issue, not a Jellyfin issue. I've thrown at it pretty much any standard format and it plays it fine. Any specific format and/or codec you're trying to play? For instance AV1 files play just fine on Jellyfin, but if the hardware doesn't support hardware decoding (which is the case foe my Nvidia Shield) it won't play well at all.
Regarding Jellyfin's themes, not saying no to some improvements, but what stops you(or others) from using it?
I personally use Jellyfin for multiple hours a day (as do friends and family, with zero complaints), almost every day and it plays my media on literally any platform (including remotely), but I don't find myself looking at Jellyfin per se for any large amount of that time - It's easy to navigate which from a UX perspective generally trumps looks when it comes to these things. I like how it looks as it's functional and easy to get to the media you want whilst showing all the nice metadata (images, sinopses, etc). What's missing?
Self-hosted Matrix.
It still needs polish, but it's on a good path. Meanwhile others are centralized by a single authority with an easy target painted on them for government coercion along with multiple other attack surfaces, and even information easily traced to PII. Also, not everything is encrypted. A lot of metadata is left out of E2EE. And those servers/providers have that data.
By contrast, a drop in the ocean is far more likely to not be targetted from the outset, making pretty much any matrix server (potentially with the exception of the matrix.org one, but it's ok to treat it as a demo anyway) a really good choice in that sense.
Element already has screensharing.