Maintenance: add biome to project (testing package)

[dreamorosi]

Summary

With #2791 being merged, we can now migrate the packages/testing workspace to use Biome.

As part of the migration I will fix any issue/inconsistency that arises. I'll do my best to minimize changes and leave the logic untouched.

Why is this needed?

So that we can gradually replace eslint, prettier, and all their dependencies with a single one, @biomejs/biome.

Which area does this relate to?

Other

Solution

No response

Acknowledgment

• This request meets Powertools for AWS Lambda (TypeScript) Tenets
• Should this be considered in other Powertools for AWS Lambda languages? i.e. Python, Java, and .NET

Future readers

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[github-actions]

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