feat(event_badge): Improve event_id handling in badge data processing

Refactor how  is ensured in badge objects when fetched from the API and cached locally.

Previously,  directly injected  into results, creating an inconsistency with other data fetching functions. This change centralizes the  injection logic within .

- Updated  to accept an optional  parameter.
- Added logic within the processor to set  and  on badge objects if they are missing, using the provided  context.
- Modified call sites (, , ) to pass the  to the  function.

This ensures consistent and robust handling of the  across badge-related data operations, aligning with the project's data processing patterns.

src/lib/ae_events/ae_events__event_badge.ts

@@ -140,6 +140,7 @@ export async function load_ae_obj_li__event_badge({
                 if (try_cache) {
                     const processed_obj_li = await process_ae_obj__event_badge_props({
                         obj_li: badge_obj_li_get_result,
+                        event_id,
                         log_lvl
                     });
                     await db_save_ae_obj_li__ae_obj({
@@ -220,6 +221,7 @@ export async function create_ae_obj__event_badge({
                 if (try_cache) {
                     const processed_obj_li = await process_ae_obj__event_badge_props({
                         obj_li: [event_badge_obj_create_result],
+                        event_id,
                         log_lvl
                     });
                     db_save_ae_obj_li__ae_obj({
@@ -510,6 +512,7 @@ export async function search__event_badge({
                 if (try_cache) {
                     const processed_obj_li = await process_ae_obj__event_badge_props({
                         obj_li: badge_obj_li_get_result,
+                        event_id,
                         log_lvl
                     });
                     await db_save_ae_obj_li__ae_obj({
@@ -686,9 +689,11 @@ async function _process_generic_props<T extends Record<string, any>>({
 // Updated 2025-10-06
 export async function process_ae_obj__event_badge_props({
     obj_li,
+    event_id,
     log_lvl = 0
 }: {
     obj_li: any[];
+    event_id?: string;
     log_lvl?: number;
 }) {
     return _process_generic_props({
@@ -696,6 +701,12 @@ export async function process_ae_obj__event_badge_props({
         obj_type: 'event_badge',
         log_lvl,
         specific_processor: (obj) => {
+            // If the event_id isn't returned from the API, add it here.
+            if (event_id) {
+                if (!obj.event_id) obj.event_id = event_id;
+                if (!obj.event_id_random) obj.event_id_random = event_id;
+            }
+
             // Event badge-specific computed sort fields, overriding generic ones if needed
             obj.tmp_sort_1 = `${obj.group ?? ''}_${obj.priority ? '1' : '0'}_${
                 obj.sort?.toString().padStart(3, '0') ?? ''