For Fintunes, it's worth asking where you downloaded it from. Was it F-Droid?
I'm part of the Jellyfin Core Team, and for our own official app, the normal one (sideloaded APK or Google Play) has Cast support, while the F-android version doesn't. It's because Casting relies on a Google proprietary SDK module.
To this day we have no idea why. If anyone has any suggestions, I'm all ears.