Update 'Performance profiling' to use `package:integration_test`

[bryanoltman]

Page URL

https://docs.flutter.dev/cookbook/testing/integration/profiling/

Page source

https://github.com/flutter/website/tree/main/src/cookbook/testing/integration/profiling.md

Describe the problem

Docs reference flutter_driver but doesn't include installation instructions (i.e., flutter pub add 'dev:flutter_driver:{"sdk":"flutter"}'). It also seems like flutter_driver is deprecated based on https://docs.flutter.dev/release/breaking-changes/flutter-driver-migration, but it's not clear how one would do performance profiling with only the package:integratin_test.

Expected fix

Docs either better explain how to get started with flutter_driver or provide a package:integration_test-only alternative.

Additional context

No response

I would like to fix this problem.

• [ ] I will try and fix this problem on docs.flutter.dev.