This has multiple side effects, including typing when rebinding a key and being unable to unbind a key.
Version is Controlling-fabric-1.18.2-9.0+22.jar

I'm unable to reproduce, simply clicking off the search box deselects it.

I'm using Controlling-forge-1.18.2-9.0+22 and have been able to get it happen with debugify installed. Attempting to change a key bind but clearing the keybind with ESC key can then cause the search box to capture input focus of the keyboard and wont release it. happened with the latest 3 versions of Debugify installed. removed the mod and its stopped happening.

Report that to them, after testing it myself, they seem to be doing weird things with edit box focus, it seems as if a screen has at-least one EditBox, then at-least one of them needs to be focused at all times? No idea what they are trying to solve, if anything I feel as though they have introduced a bug.