You'll probably have a local domain for you're Jellyfin container, resolved via Pi-hole (something like jellyfin.box). And when casting from the Jellyfin app to a Chromecast, the screen is stuck on the Jellyfin logo.
This is because the Chromecast can't resolve jellyfin.box. Chromecast has its DNS-servers hard coded to Google's DNS-servers.
To resolve this i rerouted 8.8.8.8 and 8.8.4.4 in my router to my local DNS server (Pi-hole).
In FRITZ!Box you do this via Home Network > Network > Network Settings > Static Routing Table and open IPv4 Routes. There you can add 2 static routes.