[SainathPoojary]

When you delete the last term in a search result on the Tags or Categories screen, the search box disappears, so you can't change or clear the search.

This keeps the search box visible while a search is active (an s parameter is in the URL). It is still hidden when there are no terms and no search, which matches WP_List_Table::search_box().

Testing:

1. Go to Posts → Tags and search for a term with one result.
2. Delete it. The search box should stay visible.
3. Clear the search and delete all tags. The search box should be hidden.

Trac ticket: https://core.trac.wordpress.org/ticket/66672

Before:

Screen.Recording.2026-11-12.at.4.28.26.PM.mov

After:

Screen.Recording.2026-11-12.at.4.29.10.PM.mov

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