chore: add assertions to integ tests using AwsCustomResource (#29950)

Closes #29937 

### Reason for this change

Adding assertions for `AwsCustomResource` will improve our test coverage.

### Description of changes

Added assertions for `AwsCustomResource` to integ tests that were impacted by this [PR](#29868).

### Description of how you validated changes

Assertions were validated by running the integ tests and verifying that it succeeded.

### Checklist
- [x] My code adheres to the [CONTRIBUTING GUIDE](https://github.com/aws/aws-cdk/blob/main/CONTRIBUTING.md) and [DESIGN GUIDELINES](https://github.com/aws/aws-cdk/blob/main/docs/DESIGN_GUIDELINES.md)

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*By submitting this pull request, I confirm that my contribution is made under the terms of the Apache-2.0 license*