Thank you to the viewer who suggested I make this video. Unfortunately, I couldn't find your original comment to thank you by name. There is some inadvertent mic brushing by my scarf (the earphone cable kept hitting the mic so I wasn't able to monitor my sound) but I hope it doesn't bother anyone :-)
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