Search page flickers no results -> results

What does this MR do and why?

Previous implementation of the regex button caused reload on load of the search page in the case that the regex button was pressed/enabled. Current fix shifts this to earlier stage of page and therefore doesn't cause the page reload.

MR acceptance checklist

Please evaluate this MR against the MR acceptance checklist. It helps you analyze changes to reduce risks in quality, performance, reliability, security, and maintainability.

Screenshots or screen recordings

Before	After
before-720	after-720

How to set up and validate locally

1. Enable regular expression feature flag

   echo 'Feature.enable(:zoekt_exact_search)' | rails c

2. Make sure advanced search is installed and enabled
3. Make sure you enable zoekt.
4. Click search button anywhere in gitlab ui and search any term, press enter.
5. Observe page not flickering with zoekt and regex search enabled.

Related to #458094