Just a thought, but since someone else in the thread said you can stream to Chromecast via VLC, you can desktop capture natively in VLC and stream that to your Chromecast. I can’t remember if the native capture can do sound or not, but if not, you can instead use OBS virtual cam (you’ll need v4l2loopback for the virtual cam to show up), and open that as a capture device in VLC. You should be able to attach an audio source to that as well. While I haven’t personally tested it with audio, I have used OBS virtual cam with VLC before, and it worked flawlessly for me. If you can’t find a more elegant solution, then it’s worth a shot to try and see if it works
Can you paste the output of the build so we can see what specific package it is missing? Qt is not a single package, and it’s very likely that you need the developer package
qt-devel
and its associated libraries to build, not just the base package.