fix: continue cleanup after shutdown deadline

main.go

@@ -47,7 +47,20 @@ func shutdownAll(ctx context.Context, cancelRoot context.CancelFunc, steps ...sh
 	defer cancelRoot()
 	var shutdownErr error
 	for _, step := range steps {
-		if err := step.run(ctx); err != nil {
+		done := make(chan error, 1)
+		started := make(chan struct{})
+		go func() {
+			close(started)
+			done <- step.run(ctx)
+		}()
+		<-started
+		var err error
+		select {
+		case err = <-done:
+		case <-ctx.Done():
+			err = ctx.Err()
+		}
+		if err != nil {
 			log.Printf("[main] %s shutdown: %v", step.name, err)
 			shutdownErr = errors.Join(shutdownErr, fmt.Errorf("%s shutdown: %w", step.name, err))
 		}