I was about to complain again cause after testing it on a Samsung TV (never worked there) and uninstalling bloatware like TikTok manually with phone it stopped working again on my main TV (Hisense). It's driving me crazy cause I don't know the root of it.
Downloading the APK worked however. Thanks for this simple but powerful tip. Maybe it's an issue with permission or something similar. I can't find the Cast app itself in my settings but during the installation I had to set them and installing the APK also didn't update the app which is weird I think. It's more like it replaced it.
Does anyone know how I can access the Cast app and its settings? Maybe this will help in future.