I’m running into the same issue, but on Windows. Initially I thought minimizing the windows would unfreeze it, but I tried what you said, moving or resizing, and sure enough, that too unfreezes it.
My post was here: Brave UI freezes while watching YouTube videos at random intervals - Browser Support - Brave Community
In my case, I always have a YouTube video playing in the background. Do you by chance also have a YouTube video playing? I’ve noticed for me, the window that causes the freezing most (therefore the one that needs to be moved, resized or minimized to unfreeze) is always seemingly YouTube, but other Brave windows will not unfreeze it, only the window that has YouTube playing.