NOTE: This is Take 2 of the video that I made last night. I'm closer to the microphone in this video. We'll look at the same items again, with a bonus mini item at the very end. Hopefully you'll like this one better.
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