Fix flakyness of GUI tests
Fixes #98163.
All flaky tests seemed to be linked to the search. Since the search JS is loaded when we focus the search input, I think it's possible that we enter faster than the JS is actually loaded. The solution for that would be to do it in two steps: first we write into the search input (`browser-ui-test` adds a small sleep time after such commands) and then we press enter to be sure that it wasn't missed.
cc `@JohnTitor`
r? `@Dylan-DPC`