Oh you're going to love this: There's an extension that launches custom programs with the current page as an argument, and I use it to launch mpv, which is then configured to open full-screen on the second screen with a high-quality stream of the YouTube video I'm on.

I have also configured the window to always stay on top and to resize to a small window on the bottom right, so if I press escape while the window is focused, I get picture-in-picture.

Also, mpv exits when it's done, so it's a great way of watching a video in full screen on the second monitor at the press of a button.