This addon just does one very simple thing, which is to automatically clear the Firefox search bar after you run a search. Useful for quickly pasting text into the searchbar, or for keeping your most recent query hidden.
On Linux, keeping the searchbar clear allows middle-click-pasting text into it, when otherwise the selection buffer would be clobbered when you select the old query to delete it.
"Clear Search 2" is based on the "Clear Search" add-on by samjjordan, which unfortunately no longer seems to be maintained.