YSK: You can install an extension on Firefox (android) that allows you to play YouTube videos with your screen locked: (perfect for listening to obscure music)
It can be a bit buggy at times, but when it comes to just playing music with the screen locked, it's perfect.
Edit: I forgot to also mention that ad blocker extensions make sailing the seas on mobile much more manageable. Extentions, in general, have been a really nice addition.
I've used most of these and quite frankly they are not good. Each of them quit working randomly or wouldn't play certain tracks and wouldn't get an update for days or weeks, at which point I'd move on to the next and get exactly the same experience. They're FOSS apps, and I'm fairly certain Google is to blame for breaking them, but even so if they are unusable for days or weeks at a time I cannot recommend them.
If you just want a YouTube app with no ads and background playback I would recommend PipePipe. It's what I've settled on after trying everything else, and it's fantastic. Google breaks it all the time, but updates very quickly bring it back online.
If you want something FOSS that's closer to the YT Music experience, I don't know what to tell you.
RiMusic is update regularly, no third party player is perfect, even PipiPipe or Newpipe can break suddenly, Google/YouTube don't like third party apps using their services and are always implementing ways to break apps
I'm pretty sure extensions can request browsing data for some specific URLs rather than every site you visit. If an extension with functionality on one website asks for access to all of them, then yeah it's a bad sign.
The person you replied to is correct, and your link confirms it:
An extension with broad permissions can access all tabs and browsing data
The extension does not just have this access, it has to request it from the user first.
Of course, an extension can request access to all browsing data, but Firefox will tell you about that before you install it. And better still, the extension this post is about, doesn't even request this: