I just want to say that I am in exactly the same shoes as OP. Brave has two features that I currently miss. I can play YouTube and YouTube Music in the background and it also works with Apple CarPlay. I wish those two features could be implemented. Thank you!
Edit: I just noticed a funny workaround for background play. It even works with playlists in YouTube Music to play the next song after the current one is finished. You press play on the content, then you press the Vivaldi icon to open the options menu now when you swipe up the Apple bar to get to the home screen it will keep the audio channel open, it will pause it but through the Dynamic Island or Notification pull down you can resume the audio and it will keep playing in the background. Now I just wish there was a way to check a box in the settings to just make it work natively without this workaround.