When the focus is not on the search field, starting typing gives it the focus automatically, which is cool.
Typing the Backspace key on the other hand does not give focus to the search field (even though it has no other use in overview mode).

Steps:
- go in overview mode (for instance with Super key);
- type something, ex: "gimp"
- move the focus with the arrow key
- hit the Backspace key.

Result: nothing happens.

Expected result: focus should be given back to the search field and the last letter should be deleted ("gim" should be written there).

Note: of course, if the cursor was not at the end or some selection were done before focus moved, I would expect these to be taken into account in the "usual" way (selection deleted, etc.).