(Sorry if the keyboard is too loud. I'm still experimenting with my setup.) It's movie day every Saturday at your local library! Bring your ticket and come enjoy the show!
To listen while using other apps, switch the player to Picture-in-Picture (PiP) during playback — it keeps playing in a small floating window (the screen stays on).
To listen with the screen fully off, in-browser playback stops by YouTube's design. Open the video in the YouTube app to keep listening where background playback is supported (e.g. with YouTube Premium).
Open in YouTube app