Went with this extension first since it is recommended by Mozilla, but it didn't work for me at all on my Motorola phone. After trying many similar ones in the add-ons store, the best I've found so far is:
1. Background Playback Helper (YouTube & Vimeo) by phase3
2. Background Video Player by Dr. B. R. Shriradhakrishnasharnam

Hopefully this helps someone save some time. This is an older extension and hasn't been updated in more than a year and a half despite YouTube's recent changes to target non-premium users. There appear to be many newer ones, like those above, that work better based on my testing.

Recently it breaks quite substantially youtube: it everytime I reopen the site while a video is playing, it's in landscape. Also when I pass from a page to another

Not working with the screen locked for me. Next video will attempt to play for about 2 seconds, then stop until I unlock the phone again.

It stops after a random duration, sometime 10 minutes, sometime not even 1. Very annoying when you listen to a music playlist

Meh. More miss than hit

Used to work great for playing Youtube.com at night to help me sleep now since 2 weeks or so ago it stops auto playing the next video then I get a phone error thinking it doesn't have internet when I do and everything else works.

My phone plan has been overcharged when I turned on Youtube video loading infinitely and I slept

Doesn't work on Instagram reels

When the smartphone is locked, YouTube continues to play in the background for about 5 minutes, then stops. If you just minimize the browser, but do not block the smartphone, then everything is fine.
This began to happen in Firefox v122.0. Without the add-on it doesn't play at all in the background.

Used to work like a charm, but just now it stopped. It will play in the background for about 5 min then stop, even glitching Firefox and forcing me to restart it.

Used to work flawlessly but now frequently stops playing in the background (YouTube.com)

Was working until yesterday. Now stops working around 1 minute into the video when you turn the screen off or when you minimize the app..

From an Android

Audio stuttering when phone screen off or firefox not in focus. Returns to normal instantly when I give it focus. Only other addon is uBlock Origin. Anything I can do to fix this?

Leider funktioniert die Hintergrund Wiedergabe bei Youtube seit einiger Zeit nicht mehr richtig. Dieses Problem macht die Nutzung deutlich schlechter. Gibt es eine Lösung für das Problem?

From last week, it doesn't work. What should i do?

Too much battery usage. It needs an optimisation.

Doesn't work very well. It won't change to the next video most of the times. When I click on a video, or it plays automatically the next one, I often have to refresh the page. Some other little things like this. Just doesn't work that well. On youtube*

YouTube background play suddenly stops many times. When we open the browser and check the YouTube site only white screen is showing

Add-on stops all time. Please fix it 🙏