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/git-host.ts

@@ -41,6 +41,15 @@ export interface GitHost {
   /// Delete a blob from the repo. Currently identical to deleteFile;
   /// kept distinct for symmetry with putBlob.
   deleteBlob(path: string, message: string): Promise<void>;
+
+  /// Cached sync metadata, populated by the `sync` handler — get_vault_status
+  /// reads these without any network call. lastSyncAt is unix SECONDS (or null
+  /// until the first sync). ahead/behind exist for parity with `relicario
+  /// status`; the extension writes straight to the host (no local commit
+  /// graph), so in practice they stay 0.
+  lastSyncAt: number | null;
+  ahead: number;
+  behind: number;
 }
 
 /// Pre-base64 byte size at which putBlob switches from Contents API to