You can open the Play Store on the Chromecast 4th generation (the one with Google TV), and from that you can indeed install the Jellyfin Android TV app (as Google TV is derived from Android TV apparently). However if you try to look for a Jellyfin app from the regular “Apps” menu there is nothing. Typical Google making it super convoluted.
Networking is always fun to debug… haha. I tried to replicate your issue but was unable to. Are you using docker, kubernetes or something else? Would be helpful if you could post your docker-compose.yml, kubernetes object manifests or other relevant config.