Just sharing with you the drama I had today when trying to finish up my tingledom map. Fortunately nothing gets me down and I got it done! (And I was very lucky!!)
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