Remove search_page_vertical_nav feature flag

What does this MR do and why?

Related to #373613 (closed) and #384461 (closed)

Fully remove search_page_vertical_nav feature flag from the code. This is a large MR due to the number of spec changes.

I've separated the changes into multiple commits organized by reviewer type and hope that will help with the review:

• backend feature specs - !109837 (3d491bfd)
• backend haml - !109837 (d68f5dbf)
• frontend code and specs - !109837 (e129ee81)
• feature flag yml - !109837 (784618af)

Also attempt to fix a ~flaky-test from #385239 (closed)

Screenshots or screen recordings

N/A

How to set up and validate locally

search should function and always show the vertical navigation

1. navigate to search page in gdk
2. perform a search and verify all of the tabs are vertical and functional

MR acceptance checklist

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