Have a great day :) I had to add music in a couple spots because the copyright came up with background music that was playing in the shop... but I tried to choose music that is Soothing and appropriate :)
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