rustdoc item-type search is not (directly) reproduced by the URL

[huonw]

E.g. a search for trait: Eq is rendered in the URL as a plain Eq search. Theoretically the search parameter should be in 1-1 correspondence with the actual searches (e.g. just encoding the raw contents of the search box would be fine).

[Gankra]

Probably a duplicate (implementation-wise) of #16271