I've been running the SmartTube app on my Chromecast (and on a Fire TV) for over a year and it's fantastic. Of course, you'll need to side load it but once installed it'll update itself directly. There are lots of tutorials online covering how to side load it on various Android-based streaming sticks.

I have never seen a better youtube client than SmartTube. I recently switched from a Shield to an AppleTV 4k and the lack of SmartTube is close to a deal breaker. If android had a better jellyfin client, I would be back on the shield.