I use a dummy mannequin and real hair that reveals some crunchy hair sounds (and lots of cutting) with some comforting words to relax you for sleep... just enjoy.
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