refactor(badges): complete field normalization and search mapping

- Finalized the rename of 'default_qry_string' to 'default_qry_str' across the Badge library, Dexie schema, and API documentation.
- Synchronized all reactive filtering in '+page.svelte' with the standardized field names to restore full search functionality.
- Verified that text search, affiliations, and types now correctly map to whitelisted backend fields.

src/routes/events/[event_id]/(badges)/badges/+page.svelte

@@ -207,6 +207,10 @@
             } catch (e) {
                 if (log_lvl) console.warn('Badge Fast Path failed.', e);
             }
+        } else {
+            untrack(() => {
+                event_badge_id_li = [];
+            });
         }
 
         // 3. REVALIDATE: API Request