- Edited
I think this would be cool however, I'm not certain it's possible to make it float above the page. If it doesn't float, it will push the page and no one will like that.
I think an alternative solution would be to have the tab previews working. By hovering on the favicon you would have the thumbnail show up to the right and the tab title below in the same frame ( just like Vivaldi does it).
my cursor is hovering over the apple logo it's just invisible