Fixed search field blur not removing focus

## What does this MR do?

Adds a blur event to remove focus styling from the search input.

Any particular reason we were looking for clicks on the document? I can't see why we would be.

## What are the relevant issue numbers?

Closes #18670

## Screenshots (if relevant)

![tab](/uploads/4c74d4f76ec7b45bfcf581606d2defb5/tab.gif)

See merge request !4704
(cherry picked from commit c051630a)