The latest controversial proton redesign added new two lines tabs, however it haven't been put to great use.
I think we can do better and at the same time bring back the compact mode by merging the search bar and the tab bar.
While we put the url directly into the tabs, other icons could go in the tool bar, making a better use of the window surface.
The url is a clickable text area
and expands to show the full search bar when we start typing.