Fix: Harden V3 search logic and restore specialized business mapping

- API: Updated `search_ae_obj_v3` to correctly serialize complex URL parameters (JSON).
- Events: Restored "sacred" business logic for Event Badge and Session searches using `ft_qry` and `lk_qry`.
- PWA: Fixed manifest path in `app.html` to resolve 404 errors.
- Documentation: Updated `GEMINI.md` and `TODO.md` with recent search hardening accomplishments.

src/lib/ae_events/ae_events__event_session.ts

@@ -361,7 +361,7 @@ export async function update_ae_obj__event_session({
     return result;
 }
 
-// Updated 2026-01-21 to Restore Full Aether Search Logic
+// Updated 2026-01-21 to Restore Full Aether Search logic
 export async function search__event_session({
     api_cfg,
     event_id,
@@ -405,16 +405,14 @@ export async function search__event_session({
         console.log(`*** search__event_session() *** [V3] event_id=${event_id} ft=${fulltext_search_qry_str}`);
     }
 
-    // 1. Build the search query body
     const search_query: any = {
-        q: '', // Default query string
+        q: '',
         and: [{ field: 'event_id_random', op: 'eq', value: event_id }]
     };
 
-    // 2. Build the params object for special flags (the 'params_json' equivalent)
     const params: key_val = {};
 
-    // 3. Restore the Fulltext Logic
+    // Restore Fulltext logic
     if (fulltext_search_qry_str || ft_presenter_search_qry_str) {
         params['ft_qry'] = {};
         if (fulltext_search_qry_str && fulltext_search_qry_str.length > 2) {
@@ -425,7 +423,7 @@ export async function search__event_session({
         }
     }
 
-    // 4. Restore the 'Like' Logic
+    // Restore Like logic
     if (like_search_qry_str || like_presentation_search_qry_str || like_presenter_search_qry_str || like_poc_name_qry_str) {
         params['lk_qry'] = {};
         if (like_search_qry_str) params['lk_qry']['default_qry_str'] = like_search_qry_str;
@@ -449,7 +447,7 @@ export async function search__event_session({
         obj_type: 'event_session',
         search_query,
         order_by_li,
-        params, // Pass the special flags into the V3 params
+        params, // Important: pass through special Aether params
         limit,
         offset,
         log_lvl