Basically adding an event listener to the homepage and transform the YouTube watch url to mpv url protocol, or convert all thumbnail hrefs to mpv://, so that when a video is clicked it is played with mpv. This is what I was thinking when I come up with the idea to use url protocol for mpv. So I found this project, but not this feature.
In addition, perhaps, add a modifier hotkey like Ctrl to activate it, so that the user can go to the video page normally.