Someone mentioned it in the comments, but I definitely recommend people checking out @LuASMRx !!! He recently made a video very similar to this one (and he’s a great guy so y’all should subscribe and show some love anyways 😌)
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