Thanks for helping me prepare for this year's family reunion! We need to discuss the layout of the room and the donation box, and then we need to go over the e-mail and mailing lists.
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