2 years later and I finally have a tascam! Setting it up and editing the audio and the video took me forever. If anyone has recommendations on how to improve the sound quality, please let me know!
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