feat(ext/sw): get_vault_status handler + cached sync state (Plan C Phase 6)

Returns cached ahead/behind/lastSyncAt from the GitHost plus a live count of
active (non-trashed) manifest items. No network call — sync is user-initiated;
the sync handler records lastSyncAt (unix seconds). ahead/behind stay 0 in the
extension (writes go straight to the host, no local commit graph) and exist
for parity with relicario status.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

extension/src/service-worker/gitea.ts

@@ -20,6 +20,9 @@ export class GiteaHost implements GitHost {
   private keysUrl: string;
   private branch: string = 'main';
   private headers: Record<string, string>;
+  lastSyncAt: number | null = null;
+  ahead = 0;
+  behind = 0;
 
   constructor(hostUrl: string, repoPath: string, apiToken: string) {
     // Remove trailing slash from hostUrl