If you enjoy whiteboard writing sounds, but not when the pen makes the familiar "high-pitch noise" from pressing too hard against the board, then skip to 16:33 when I start using the pen more lightly.
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