The Fall Festival (AKA Halloween) is growing close, so of course you want to go and get a pumpkin to carve. (Oh my, I had a lot of trouble with this one. It refused to download, and I nearly lost the audio.
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