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/lib/ae_events/ae_events__event_badge.ts

@@ -381,7 +381,7 @@ export async function search__event_badge({
     const params: key_val = {};
 
     // Standardized Text Search Pattern (V3 API)
-    // NOTE: Using 'default_qry_str' (Strict DB Column) instead of 'default_qry_string'
+    // NOTE: Using 'default_qry_str' (Strict DB Column)
     if (fulltext_search_qry_str && fulltext_search_qry_str.trim().length > 0) {
         const qry = fulltext_search_qry_str.trim();
         search_query.and.push({ field: 'default_qry_str', op: 'like', value: `%${qry}%` });
@@ -508,7 +508,7 @@ export const properties_to_save = [
     'external_event_id',
     'external_id',
     'external_person_id',
-    'default_qry_string',
+    'default_qry_str',
     'alert',
     'enable',
     'hide',

src/lib/ae_events/db_events.ts

@@ -820,7 +820,7 @@ export class MySubClassedDexie extends Dexie {
                 affiliations, affiliations_override,
                 badge_type, badge_type_code, badge_type_code_override, badge_type_override,
                 external_event_id, external_id, external_person_id,
-                default_qry_string,
+                default_qry_str,
                 alert,
                 tmp_sort_1, tmp_sort_2,
                 print_count, print_first_datetime, print_last_datetime,