[CQ] remove defunct and unused integration tests (#8179)

As mentioned in the issue, these are not current, unused and not in the
project source root (so not compiling):


![image](https://github.com/user-attachments/assets/1ac80bf4-914b-4840-aa60-3085fdceb205)


Fixes: #8088



---

- [x] I’ve reviewed the contributor guide and applied the relevant
portions to this PR.

<details>
  <summary>Contribution guidelines:</summary><br>

- See our [contributor
guide]([https://github.com/dart-lang/sdk/blob/main/CONTRIBUTING.md](https://github.com/flutter/flutter/blob/main/docs/contributing/Tree-hygiene.md#overview)
for general expectations for PRs.
- Larger or significant changes should be discussed in an issue before
creating a PR.
- Dart contributions to our repos should follow the [Dart style
guide](https://dart.dev/guides/language/effective-dart) and use `dart
format`.
- Java and Kotlin contributions should strive to follow Java and Kotlin
best practices
([discussion](#8098)).
</details>

Author: pq