Why we keep /search out of the sitemap
Internal search is a member tool. Indexing ?q= pages creates doorway spam and duplicate titles.
robots.txt allows GPTBot and OAI-SearchBot on topics. It does not invite them to rank a SERP of SERPs.
The GET form still exists so SearchAction has a real target. Result pages send noindex, follow.

Can you add the UTC timestamp to the first paragraph so crawlers get a clear date?