Switch inverted index from stale check to incremental updates

Register a hook with the indexer so that file add/remove events
incrementally maintain the inverted index, removing the need for
periodic staleness checks and cooldowns. Rebuild the index once on
startup via init_inverted_index().

backend/indexer.py

@@ -599,6 +599,11 @@ def _remove_file_from_structures(vault_name: str, rel_path: str) -> Optional[Dic
         path_index[vault_name] = [p for p in path_index[vault_name] if p["path"] != rel_path]
 
     _index_generation += 1
+
+    # Notify inverted index for incremental update
+    if _on_index_change:
+        _on_index_change('remove', vault_name, rel_path, removed)
+
     return removed
 
 
@@ -666,6 +671,10 @@ def _add_file_to_structures(vault_name: str, file_info: Dict[str, Any]):
 
     _index_generation += 1
 
+    # Notify inverted index for incremental update
+    if _on_index_change:
+        _on_index_change('add', vault_name, file_info["path"], file_info)
+
 
 async def update_single_file(vault_name: str, abs_file_path: str) -> Optional[Dict[str, Any]]:
     """Re-index a single file without full rebuild.