refactor(badges): standardize reactive search and fix text filtering

- Corrected 'search__event_badge' to use the valid 'default_qry_str' field name, resolving 400 errors during text search.
- Re-implemented the standardized debounced search pattern in '+page.svelte' with a robust Search Guard to eliminate loops.
- Hardened Fast Path local filtering to match the 'Badge' schema and synchronized result sorting with API revalidation.
- Updated 'ae_comp__badge_search.svelte' and 'ae_comp__badge_obj_li.svelte' to align with the shared data pattern and fixed Lucide icon imports.
- Ensured 'events_loc' store initialization for new search-related fields.

src/lib/stores/ae_events_stores.ts

@@ -92,6 +92,10 @@ const events_local_data_struct: key_val = {
         fulltext_search_qry_str: null,
         search_badge_type_code: null,
 
+        // New additions for search stabilization (Standardized Pattern 2026-01-27)
+        search_version: 0,
+        qry__remote_first: false,
+
         // New additions for filter states
         qry_printed_status: 'all', // Default to all
         qry_affiliations: null, // Default to null for no filter