After recording this, I immediately noticed there was a weird electronic sound in the background. It's not the camera so I'm gonna do some detective work and see what's making the noise (Probably one of my consoles :P) Thanks, guys!
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