Disclamer: videos in which the author attempts to speak in languages foreign to the author do not carry any political, cultural or religious connotations, nor are they intended to offend or ridicule anyone. I just love trying to speak other languages to get a new ASMR experience :)
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