fix(db): invoke shutdown during runtime teardown

Call Database::shutdown() from async_main graceful shutdown after webhook/tunnel stop.

Add debug logs for libSQL no-op shutdown paths (no replicator and sync-not-supported).

src/db/libsql/mod.rs

@@ -333,8 +333,14 @@ impl Database for LibSqlBackend {
                 tracing::debug!("libSQL replicator flushed at frame {}", frame_no);
                 Ok(())
             }
-            Ok(None) => Ok(()),
-            Err(libsql::Error::SyncNotSupported(_)) => Ok(()),
+            Ok(None) => {
+                tracing::debug!("No libSQL replicator to flush, skipping shutdown sync");
+                Ok(())
+            }
+            Err(libsql::Error::SyncNotSupported(_)) => {
+                tracing::debug!("libSQL sync not supported, skipping flush on shutdown");
+                Ok(())
+            }
             Err(error) => Err(DatabaseError::from(error)),
         }
     }

src/main.rs

@@ -672,6 +672,8 @@ async fn async_main() -> anyhow::Result<()> {
         .as_ref()
         .map(|db| Arc::clone(db) as Arc<dyn ironclaw::db::SettingsStore>);
 
+    let db_for_shutdown = components.db.clone();
+
     let deps = AgentDeps {
         store: components.db,
         llm: components.llm,
@@ -930,6 +932,12 @@ async fn async_main() -> anyhow::Result<()> {
         }
     }
 
+    if let Some(db) = db_for_shutdown {
+        if let Err(e) = db.shutdown().await {
+            tracing::warn!("Failed to shutdown database cleanly: {}", e);
+        }
+    }
+
     tracing::debug!("Agent shutdown complete");
 
     Ok(())