[dtd] attempt to fix flaky test connected_app_service_test.dart

Bug: #60762

Change-Id: I1c4197155c9d535ea780530ab9ff0ae9462bf5e5
Reviewed-on: https://dart-review.googlesource.com/c/sdk/+/433741
Auto-Submit: Kenzie Davisson <[email protected]>
Commit-Queue: Ben Konyi <[email protected]>
Reviewed-by: Ben Konyi <[email protected]>

Author: kenzieschmoll

pkg/dtd/test/utils.dart

@@ -70,7 +70,6 @@ class DartCliAppProcess {
 
   Future<TestProcess> start() async {
     final tmpDir = Directory.systemTemp.createTempSync();
-    addTearDown(() => tmpDir.deleteSync(recursive: true));
 
     // A simple Dart command line app that will never exit.
     const fileName = 'app.dart';
@@ -97,6 +96,10 @@ void main() async {
 
     addTearDown(() async {
       await process!.kill();
+      // Delete [tmpDir] after [process] is killed. Otherwise, the call to
+      // `tmpDir.deleteSync` may fail with an error: "The process cannot access
+      // the file because it is being used by another process."
+      tmpDir.deleteSync(recursive: true);
     });
 
     String? uri;