Order of buttons in headerbar is against the HIG
The Search button in the header bar is on the left side, while in other GNOME apps it commonly is on the right. Similarly the new tab button is on the right while the HIG recommends "New" buttons to be on the left (https://developer.gnome.org/hig/stable/header-bars.html.en, under Additional guidance).
Therefore I want to suggest swapping the two buttons.
Edited by Andre Klapper