I enjoy I listening to youtube videos with my phone screen turned off and the device locked. This is especially useful for security, battery life, and convenience.
You'll need to request the desktop site for a video, and then madly fiddle with the play button while trying to exit safari or whatever browser you use. Often, Apple will pull up their Music app when you try to get the video to keep playing. But it will work, and you can stream the video with your screen off. I will try to figure out a better solution, because my old method below does not actually work anymore for the mobile site. Rather than sending an MP4, it appears they're using some streaming system, which is more difficult to work with.
It's not something that I necessarily discovered or figured out. Rather, I have managed to defeat the technological barriers implemeneted by Apple and YouTube that restrict my freedoms. So anyway, you basically have to break the webpage with Adguard or some other content blocker, and then you request the desktop site, and you get a nice little video. Boom. Simple. It starts playing, and you can go use another app or lock your phone and save battery life with a dead screen.
Sometimes you have to fiddle with the control center to get it to play, but it works! No need to buy YouTube red or watch ads!!!! HAAHAHAHAHHAAHAHAHAHA
By the way, I love Adguard Pro (costs $2) but would also recommend their free DNS service. It's less powerful, though it still blocks a lot of stuff, and it doesn't require you to install any software, unless your phone prevents you from changing your DNS manually. In that case, you're probably using a Samsung Android, and you'll have to install a DNS changing app.