fix: API JSON error responses + navbar with dropdowns

- Add backend/libs/go-http-errors for consistent JSON errors
- REST API: use writeMethodNotAllowed, writeNotFound, writeInternalError
- middleware, gateway, search: use httperrors.WriteJSON
- SPA: navbar with Explore/Tools/More dropdowns, initNavDropdowns()
- Next.js: Navbar component with dropdowns + mobile menu

Co-authored-by: Cursor <cursoragent@cursor.com>

backend/api/rest/errors.go

@@ -49,3 +49,8 @@ func writeForbidden(w http.ResponseWriter) {
 	writeError(w, http.StatusForbidden, "FORBIDDEN", "Access denied")
 }
 
+// writeMethodNotAllowed writes a 405 error response (JSON)
+func writeMethodNotAllowed(w http.ResponseWriter) {
+	writeError(w, http.StatusMethodNotAllowed, "METHOD_NOT_ALLOWED", "Method not allowed")
+}
+