I bought myself a new camera! Yes, it is expensive, but I have saved up for a while for this! It is the Sony Nex f3 if anyone is wondering! there are some breathing noises but i will try to fix that for next time :)
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