I think it used to work like that, but since we upgraded to 22.2 it doesn't? It works with the Finder Search though.
I checked 22.1 and it behaves the same as 22.2, and it is only the initial search entry than clears with ESC. What version did you upgrade from?
It's 21.2. Honestly I don't know anymore if it worked that way, I don't have this version anymore. I just remember that I talked to Patrick about this or something similar a long time ago and he said, oh yeah just hit Esc.
No matter what it should work the same like with the Finder Search. Esc deletes it and if you would simply select the last search I could immediately overwrite it by typing the new search term. But this should be an additional feature. ESC should work in Page Search and Finder Search out of UX