I love the top gear reference, but surely May would have been the obvious choice, Hammond is just asking for a crash!

This whole episode is giving me flashbacks to the ActiveX days.

The tyranny of the default.

“Here mum, I’ve installed Firefox for you, it’s better than Chrome in every way!”
“My knitting circle website doesn’t work, I can’t download patterns, it says I need Chrome”

Internet Explorer was effectively abandon-ware for a decade after Microsoft used their OS pseudo-monopoly to crush Netscape.
It took another tech giant abusing THEIR monopoly to relegate IE to the trash heap it should have already been on.

Comforting and Terrifying.
Comferrifying?
Terriforting?

So you won’t use your banks website?
Or your utilities (gas/water/electricity/internet)?
You won’t let your kids use the portal at their school for submitting assignments?
Your government sites for renewing your drivers license or scheduling hard refuse pickup?

I can think of lots of reasons that will force me to have chrome installed if this goes ahead.

I can’t see that log, the url appears to be truncated.
This is a weird one.
I assume your movie library in Jellyfin is targetted at the root? /media/Filme ?
I also assume you have your localisation set to french, have you tried temporarily setting it to us english and restarting the docker instance?
I’ve seen weird things happen if the docker instance starts before the mount, so if /data/Filme is a mount, it’s worth manually restarting your instance:
sudo docker restart jellyfin

Do you have nested libraries? Like a library pointed at /media and another one pointed at /media/Filme and maybe another at /media/Filme/Comedies ?
https://github.com/jellyfin/jellyfin/issues/8518

I’m pretty sure Firefox doesn’t know how to cast, that’s a chrome feature.
Secondly, a chromecast dongle can either be targetted locally by an app (such as chrome) or over the internet via https.
If you are just hosting on your windows laptop, you probably don’t have a domain with TLS, yes?
From localhost (the laptop itself), if you run chrome, you can probably cast to your dongle whilst on the same LAN.

If you have one of the newer Chromecasts with the remote, you can simply install the Jellyfin app on it directly, and address your Jellyfin install by IP and port.

Plex uses some fancy redirection work around these limitations, but it relies on an external service that they provide.

When you set up your libraries, it’s important that you point the path at the root folder, jellyfin expects a fairly specific naming convention.
Here’s how it is suggested to setup your tv shows for instance: https://jellyfin.org/docs/general/server/media/shows

Simplistically, lets say you have 2 shows called “Friends” and “The Witcher”, each with multiple seasons, and your NFS mount is /mnt/media.
You’d create something like: /mnt/media/tv
That’s where you’d point your tv library, at that “tv” directory. It doesn’t actually matter what the directory is called, but the library should be of type “shows”.
Under that /mnt/media/tv directory, you would create a directory for each show, and it would be the name of that show, so you’d get: /mnt/media/tv/Friends/ and /mnt/media/tv/The Witcher/
Then under those directories you would create seasons, to put your episodes in, ie /mnt/media/tv/The Witcher/Season 01/The Witcher - 01x01 - The End’s Beginning.avi
/mnt/media/tv/The Witcher/Season 01/The Witcher - 01x02 - Four Marks.avi

If you pointed the root of your library at /mnt/media/tv/The Witcher/Season 01/, it would probably fail to parse the episodes.
If you create your library as /mnt/media/allmystuff/ and just ram everything in there, it’s unlikely to find anything.
This may all seem a bit complicated, but there’s lots of tools that are useful to automate this process.
I personally recommend https://sonarr.tv/

If you are doing all of the above correctly, we’ll have to dig a bit deeper for more details.

As for “unsupported formats”, that most commonly happens when you have enabled hardware acceleration and it’s not working properly.
Whilst there’s several reasons why it may not be working, to rule it out, try temporarily disabling Hardware Acceleration under Dashboard -> Playback -> Transcoding.
The system should fall back to CPU transcoding which may be slow (hardware dependent), but at least it should function.

The first 90% of the task takes 90% of the time.
The last 10% of the task takes the other 90% of the time.

I never owned a console, but I distinctly remember playing this, so there must have been a PC port some time in the early 90s.

Classic game.