[video_player] `drive examples` tests timing out

https://ci.chromium.org/ui/p/flutter/builders/prod/Mac_arm64%20ios_platform_tests_shard_5%20stable/4054/overview
https://ci.chromium.org/ui/p/flutter/builders/prod/Mac_arm64%20ios_platform_tests_shard_5%20stable/4062/overview

The `drive examples` step is timing out for video_player:

```
============================================================
|| Running for packages/video_player/video_player [@0:06]
============================================================
Running command: "flutter test -d 0745FD37-E11A-437D-AC97-0304A6925B3B --debug-logs-dir=/Volumes/Work/s/w/ir/x/w/rc/flutter_logs_dir integration_test" in /Volumes/Work/s/w/ir/x/w/packages/packages/video_player/video_player/example
Resolving dependencies...
Downloading packages...
_fe_analyzer_shared 93.0.0 (99.0.0 available)
analyzer 10.0.1 (12.1.0 available)
dart_style 3.1.7 (3.1.8 available)
meta 1.17.0 (1.18.2 available)
test 1.30.0 (1.31.0 available)
test_api 0.7.10 (0.7.11 available)
test_core 0.6.16 (0.6.17 available)
vector_math 2.2.0 (2.3.0 available)
Got dependencies!
8 packages have newer versions incompatible with dependency constraints.
Try `flutter pub outdated` for more information.
00:00 +0: loading /Volumes/Work/s/w/ir/x/w/packages/packages/video_player/video_player/example/integration_test/controller_swap_test.dart
To ensure your app continues to launch on upcoming iOS versions, UIScene lifecycle support will soon be required. Please see https://flutter.dev/to/uiscene-migration for the migration guide.
Warning: Missing build name (CFBundleShortVersionString).
Warning: Missing build number (CFBundleVersion).
Action Required: You must set a build name and number in the pubspec.yaml file version field before submitting to the App Store.
Running Xcode build...
Xcode build done. 20.6s
Test is taking a long time, taking screenshot test-timeout-screenshot_integration_test.png...
Running command: "flutter screenshot -d 0745FD37-E11A-437D-AC97-0304A6925B3B --out=/Volumes/Work/s/w/ir/x/w/rc/flutter_logs_dir/test-timeout-screenshot_integration_test.png" in /Volumes/Work/s/w/ir/x/w/packages/packages/video_player/video_player/example
Screenshot written to ../../../../../rc/flutter_logs_dir/test-timeout-screenshot_integration_test.png (66kB).
```

Start with packages/video_player/video_player/example/integration_test/controller_swap_test.dart and the integration_test suite shown in the CI logs. Reproduce the drive examples step on the affected iOS configuration and inspect where the test stops responding. Done means the video_player drive examples integration tests complete without timing out.

Written by the indexing model from the issue text.