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

src/lib/stores/ae_events_stores__badges.svelte.ts

@@ -0,0 +1,18 @@
+/**
+ * ae_events_stores__badges.svelte.ts
+ *
+ * Svelte 5 PersistedState store for Badge module local config.
+ * Replaces the `events_loc.badges` sub-object from the Svelte 4 persisted store.
+ *
+ * localStorage key: 'ae_badges_loc'
+ * Version gate:     AE_BADGES_LOC_VERSION in store_versions.ts
+ *
+ * Usage:
+ *   import { badges_loc } from '$lib/stores/ae_events_stores__badges.svelte';
+ *   badges_loc.current.fulltext_search_qry_str   // read
+ *   badges_loc.current.search_version++           // write
+ */
+import { PersistedState } from 'runed';
+import { badges_loc_defaults } from './ae_events_stores__badges_defaults';
+
+export const badges_loc = new PersistedState('ae_badges_loc', badges_loc_defaults);