Let me fix the bull in china shop analogy here. So the meme is that a bull in a china shop won’t break anything right? Even though there’s so much fragile stuff to break around, they’ll just walk around it all… unless that is, you interfere. Then it can be a whole big stinking mess. Wait for the bull to get bored and leave.
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