Remove inline JavaScript for Search autocomplete

What does this MR do?

Remove inline JavaScript from the search partial for Search autocomplete.

Are there points in the code the reviewer needs to double check?

That this doesn't break anything (it didn't when I tested it!)

Why was this MR needed?

Inline scripts are bad, this removes a few of them.

What are the relevant issue numbers?

#18231 (closed) and #19866 (closed)

Does this MR meet the acceptance criteria?

• Tests
  • All builds are passing
• Conform by the style guides
• Branch has no merge conflicts with master (if you do - rebase it please)
• Squashed related commits together