Docs: cdk examples + e2e tests

[saragerion]

Description of the feature request

Similarly to what is done for Tracer and Metrics utilities, it would be helpful for developers to add these functionalities.

Problem statement

Summary of the feature

• Add logger related examples in root folder
• Add e2e tests in the package folder/scope

Code examples
N/A

Benefits for you and the wider AWS community
Better understand how to use the library, better testing coverage

Describe alternatives you've considered
N/A

Additional context
N/A

Related issues, RFCs

N/A

[ijemmy]

We have e2e tests for logger now (PR #529)

@saragerion I understand that we have already had logger example in examples/cdk (here).

Or do you mean moving the examples from packages/logger/examples to examples/cdk? In that case, is this duplicated with #332 (which is on-hold for customer's feedback).

[github-actions]

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