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_api/api_post__crud_search_v3.ts

@@ -14,6 +14,7 @@ interface SearchAeObjV3Params {
     limit?: number;
     offset?: number;
     delay_ms?: number;
+    params?: key_val;
     headers?: any;
     log_lvl?: number;
 }
@@ -31,29 +32,38 @@ export async function search_ae_obj_v3({
     limit = 100,
     offset = 0,
     delay_ms = 0,
+    params = {},
     headers = {},
     log_lvl = 0
 }: SearchAeObjV3Params) {
     const endpoint = `/v3/crud/${obj_type}/search`;
 
     // Hybrid search: Standard filters passed as query params
-    const params: key_val = {
+    const query_params: key_val = {
         enabled,
         hidden,
         view,
         limit,
-        offset
+        offset,
+        ...params
     };
 
-    if (for_obj_type) params['for_obj_type'] = for_obj_type;
-    if (for_obj_id) params['for_obj_id'] = for_obj_id;
-    if (order_by_li) params['order_by_li'] = JSON.stringify(order_by_li);
-    if (delay_ms > 0) params['delay_ms'] = delay_ms;
+    if (for_obj_type) query_params['for_obj_type'] = for_obj_type;
+    if (for_obj_id) query_params['for_obj_id'] = for_obj_id;
+    if (order_by_li) query_params['order_by_li'] = JSON.stringify(order_by_li);
+    if (delay_ms > 0) query_params['delay_ms'] = delay_ms;
+
+    // Serialize any complex objects in the query params (e.g. ft_qry, lk_qry)
+    for (const key in query_params) {
+        if (typeof query_params[key] === 'object' && query_params[key] !== null) {
+            query_params[key] = JSON.stringify(query_params[key]);
+        }
+    }
 
     if (log_lvl) {
         console.log('*** search_ae_obj_v3 ***');
         console.log('Endpoint:', endpoint);
-        console.log('Params:', params);
+        console.log('Params:', query_params);
         console.log('Search Query:', search_query);
     }
 
@@ -61,7 +71,7 @@ export async function search_ae_obj_v3({
     return await post_object({
         api_cfg,
         endpoint,
-        params,
+        params: query_params,
         headers,
         data: search_query,
         log_lvl