How can I control YouTube playback using voice commands?
Try a 3rd party app - perhaps one of those developers coded up their app to include Siri voice commands.

I'm not sure which ones support voice commands; let us know if you find one that does!

Some Youtube alternatives:
filmora.wondershare.com/.../youtube-app-alternatives.html

Some that allow playing music in the background, might have paid attention to this voice commands feature:
mashtips.com/youtube-music-streaming-ios-apps/