It's not a perfect solution - I have occasionally noticed it leading to some buggy behaviour in the YouTube/YouTube Music sites using Safari, but nothing anywhere near as bad as using those websites without it!
The only odd behaviour I can call to mind was one time that it continued playing audio when I answered a phone call. It was easy to stop the music playing, and the other person on the call couldn't hear the music. I was actually disappointed that the other person couldn't hear the music, and I've been disappointed every time I've taken a phone call since and the music hasn't continued playing. I wish that was a feature :)
I think Vinegar was well worth the small one-time price, and I like supporting the developer. I've heard that Brave allows playing with the screen off, but I like my setup enough that I don't want to install Brave just for that.