When I click on that, the search bar appears at the top of the screen, but at the same time the menu disappears, the window below it gets focus, and the search bar disappears. Maybe it would be better if the search bar wouldn't immediately disappear on losing focus.
I don't have focus follows mouse, but I do have wayland, and it's broken here at least.
I checked KDE 4, and the search bar doesn't disappear when losing focus there, so this is definitely a regression.
I've tested this on plasmashell 5.20.2 and I can't reproduce this issue, I set Focus follows mouse and I can use krunner when launching from kickoff. Can you please test and confirm if this issue is still occurring or if this bug report can be marked as resolved. I'm setting status to "needsinfo" pending your response, please change back to "reported" or "resolved" when you respond, thanks.
I currently have plasma 5.17, and the search bar doesn't lose focus when the kickoff menu closes, even with focus strictly under mouse. I guess this problem went away in the meantime.