fix: #3635809 Save status pip stays on "Published" after an edit

save_status.js drops the query string before classifying the request and matches /api/display-builder/{id} wherever it starts, so ?from= on a drop and a base path or path prefix (/de/, /preview/{site}/) no longer keep the pip on "Published".

save_status.spec.ts passed only because a new display already rests on "saved". It now publishes first, so the edit has to flip the pip; it fails without the fix.

AI-Generated: Yes (Claude Code drafted the fix and test; I reviewed and ran them)

Closes #3635809