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

@@ -326,6 +326,24 @@ impl Database for LibSqlBackend {
         libsql_migrations::run_incremental(&conn).await?;
         Ok(())
     }
+
+    async fn shutdown(&self) -> Result<(), DatabaseError> {
+        match self.db.flush_replicator().await {
+            Ok(Some(frame_no)) => {
+                tracing::debug!("libSQL replicator flushed at frame {}", frame_no);
+                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)),
+        }
+    }
 }
 
 // ==================== Row conversion helpers ====================

src/db/mod.rs

@@ -523,6 +523,13 @@ pub trait Database:
 {
     /// Run schema migrations for this backend.
     async fn run_migrations(&self) -> Result<(), DatabaseError>;
+
+    /// Shutdown hook for backend-specific drain/flush behavior.
+    ///
+    /// Default implementation is a no-op so existing backends remain compatible.
+    async fn shutdown(&self) -> Result<(), DatabaseError> {
+        Ok(())
+    }
 }
 
 #[cfg(test)]

src/db/postgres.rs

@@ -61,6 +61,11 @@ impl Database for PgBackend {
     async fn run_migrations(&self) -> Result<(), DatabaseError> {
         self.store.run_migrations().await
     }
+
+    async fn shutdown(&self) -> Result<(), DatabaseError> {
+        self.store.pool().close();
+        Ok(())
+    }
 }
 
 // ==================== ConversationStore ====================

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(())