Add the padding around the SearchEntry widget in the searchbar, or integrate it directly into the Headerbar
This SearchEntry widget is missing some 3px spacing above/below it so that it doesn't feel completely cramped against the edge of the headerbar above it and the listview below it:
However, given how very few things are in GNote's headerbar (and the app title is very short), a possible alternative could be to simply replace the search toggling button by a GTK SearchEntry directly, a bit like this (this is just a rough mockup):