On October 6th I turned 18! So this video is a few weeks late! Sorry that this isn't my best video (especially with all of the background noises) but I hope you enjoy 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