This was too fascinating and mesmerising to me not to share. I hope this is somewhat relaxing. Special thanks to erleichda, for advice on how to rectify the left/right channel problem. All solved! Oh, and Happy Diwali everyone!
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