Fix search group/project filtering to show results

What does this MR do?

• Typing in the project/group filter input actually filters down the list instead of showing no results
• Maintains search input state after closing and re-opening to align with the search results which were still filtered down

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

Why was this MR needed?

Screenshots (if relevant)

• Visit /search and play with group/project filter

Before

After

Does this MR meet the acceptance criteria?

• Changelog entry added
• Tests
  • Added for this feature/bug
  • All builds are passing
• Conform by the merge request performance guides
• Conform by the style guides
• Branch has no merge conflicts with master (if it does - rebase it please)
• Squashed related commits together

What are the relevant issue numbers?

Closes #26616 (closed)