chore(badges): remove legacy badge_id_only_search; sync remote badges config into badges_loc; docs update

src/routes/events/[event_id]/(badges)/badges/+page.svelte

@@ -80,6 +80,20 @@ let lq__event_obj = $derived(
     })
 );
 
+// Mirror server-side badges config into the persisted local store when the
+// event object is available so UI can read a fast local copy.
+$effect(() => {
+    const remote_cfg = $lq__event_obj?.mod_badges_json;
+    if (remote_cfg) {
+        untrack(() => {
+            events_func.sync_config__event_badges({
+                badges_cfg_remote: remote_cfg,
+                log_lvl: log_lvl
+            });
+        });
+    }
+});
+
 // Stable LiveQuery Pattern (Aether UI V3)
 let lq__event_badge_obj_li = $derived.by(() => {
     const ids = event_badge_id_li;
@@ -129,9 +143,7 @@ let search_params = $derived({
     aff: (badges_loc.current.qry_affiliations ?? '').toLowerCase().trim(),
     sort: badges_loc.current.qry_sort_order,
     event_id: $events_slct?.event_id,
-    remote_first: badges_loc.current.qry__remote_first,
-    // Event-level override: when true, restrict searches to badge IDs only
-    badge_id_only: $lq__event_obj?.mod_badges_json?.badge_id_only_search ?? false
+    remote_first: badges_loc.current.qry__remote_first
 });
 
 // 2. Controlled effect for triggering searches
@@ -194,10 +206,7 @@ async function handle_search_refresh(params: any) {
                                 return false;
                         }
 
-                        if (params.badge_id_only && qry_str) {
-                            const id = (badge.event_badge_id ?? '').toLowerCase();
-                            if (!id.includes(qry_str)) return false;
-                        } else if (qry_str) {
+                        if (qry_str) {
                             const given_name = (
                                 badge.given_name ?? ''
                             ).toLowerCase();
@@ -376,7 +385,7 @@ async function handle_search_refresh(params: any) {
 <Comp_badge_search event_id={$events_slct?.event_id ?? ''} log_lvl={1}
 ></Comp_badge_search>
 
-{#if $ae_loc.edit_mode && ($lq__event_obj?.mod_badges_json?.enable_add_badge_btn ?? true)}
+{#if $ae_loc.edit_mode && (badges_loc.current.enable_add_badge_btn ?? true)}
     <div class="flex justify-end px-4">
         <button
             type="button"