Persist search filter option after initial query

What does this MR do and why?

Fixes this bug: #1518 (closed)

Screenshots, screen recordings, or links to review app

https://gps-filter-persist.docs.gitlab-review.app/search

How to set up and validate

This can be tested on the review app, like this:

1. Run a search from anywhere on the site.
2. Select a filter option. Results filter down to that section.
3. Leaving the checkbox selected, run a new search.
4. Results should be filtered down to your previously-selected section.

If you want to test locally to compare to the main branch:

1. Check out this branch and build the site with the Google search backend:

make clean && GOOGLE_SEARCH_KEY="AIzaSyAUCkVNs7JsHYKISjVrVv1PGXg9WQr1MCQ" SEARCH_BACKEND="google" bundle exec nanoc compile

2. View the site: bundle exec nanoc view
3. Follow the rest of the steps as above.

Merge request 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 merge request.