On docs search results page, make down/up arrows select search results by auto focusing search field

[Boscop]

Before, when you opened a rust doc page by a url containing a search query, after the page loaded, you could navigate with down/up arrows through the matched symbols.
Now it doesn't work anymore, you have to use the mouse to click!
E.g. an url like https://doc.rust-lang.org/nightly/std/?search=scan or https://docs.rs/imgui/0.4.0/imgui/struct.Ui.html?search=set

Maybe the fix is as simple as putting the autofocus attribute on the search input, so that the first down arrow press selects the first search result.

CC @jyn514
@rustbot modify labels: +T-rustdoc

[camelid]

I couldn't get autofocus to work, so I'm unassigning myself.

[GuillaumeGomez]

It was rejected in #77333. Closing it then.