On Android I use Firefox with [1] and [2] for YouTube; the former lets me turn the screen off without letting YouTube know that the screen is turned off.

On my laptop, I use youtube-dl when I want to keep a personal copy, and mpv/vlc (which automatically using youtube-dl internally) when I just want to play something once.

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1: https://addons.mozilla.org/en-US/firefox/addon/video-backgro...

2: https://addons.mozilla.org/en-US/firefox/addon/ublock-origin...