fix(badges): fix search-result layout shift + unify empty/loading states

Scrollbar shift:
- Add [scrollbar-gutter:stable] to #ae_main_content in events layout so a
  scrollbar appearing on first results load no longer reflows the centered
  search form (was shifting ~8px left on Linux)

Empty/loading state consistency:
- Move search_status prop into ae_comp__badge_obj_li so it can swap its own
  empty state: spinner + "Searching..." while a search is in progress,
  UserSearch icon + prompt text otherwise
- Unify p-16 / size-3em / mb-2 / text-xl across all three states (initial
  load, searching, no results) so height never jumps between transitions
- Pass search_status from +page.svelte to the component

Transitions:
- transition:fade on initial-load spinner div
- transition:slide on Create/Upload badge button row (appears with edit mode)

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

src/routes/events/+layout.svelte

@@ -210,7 +210,7 @@ function clear_sess() {
         container m-auto flex h-full min-h-full
         w-full max-w-7xl
         min-w-full flex-col gap-1
-        overflow-auto
+        overflow-auto [scrollbar-gutter:stable]
 
         bg-gray-50 text-gray-800
         dark:bg-gray-900 dark:text-gray-200