Remove legacy header search code

What does this MR do and why?

Remove header search javascript code

This removes the legacy header search code, as the old nav cannot be used any longer.

Remove header search HAML code

This removes the legacy header search HAML code. It wasn't too much, and we could easily remove it.

Unfortunately all of the helpers used, still have usage inside of GitLab

Remove most of header search from SCSS

This removes most of the header search SCSS. There is a separate MR which removes a lot of related styles from our themes: !136891 (closed)

Screenshots or screen recordings

N/A, no user visible changes

How to set up and validate locally

N/A

MR acceptance checklist

This checklist encourages us to confirm any changes have been analyzed to reduce risks in quality, performance, reliability, security, and maintainability.

• I have evaluated the MR acceptance checklist for this MR.