Hey this is Winry here at Rockbell Repairs. It seems you've been having some problems with your automail prostheses! No worries though, I'm an expert and can fix you up in a jiffy.
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