refactor(logger): overall improvements - DX, examples, business logic

[saragerion]

Refactor in the Logger library.

Key changes

1. Inject context: removed environment variable. If it's injected, it's visible in the logs.
2. AWS request ID key renamed to function_request_id
3. Renamed all context key to start with function_*
4. Refactor of error logic to handle better errors given with a custom key
5. Persistent log keys: changed DX / example to use appendKey
6. Sample rate calculation happening and set for the scope of a logger instance, not a single log item
7. Added "refresh sample rate calculation" method
8. Added public method for setting the sample rate value

Next steps (after this PR)

TODO: Edit repo to make it contribuiting friendly

TODO: Logger - Update test suite with missing unit tests and relevant test cases/scenario

TODO: Logger - Create docs

TODO: Logger - CI/CD pipeline for publishing
TODO: Logger - Create new package for Middy middleware

Logger examples playground

To check how the logger works, checkout in this branch:
logger-feedback-improvements

And then run the example scripts in the packages/logger folder:

cd packages/logger

npm run example:hello-world
npm run example:inject-context
npm run example:inject-context-decorator
npm run example:errors
npm run example:constructor-options
npm run example:custom-log-formatter
npm run example:child-logger
npm run example:additional-keys
npm run example:sample-rate
npm run example:persistent-attributes
npm run example:ephemeral-attributes

Checklist

• Meet tenets criteria
• Update tests
• Update docs
• PR title follows conventional commit semantics

Breaking change checklist

RFC issue #:

• Migration process documented
• Implement warnings (if it can live side by side)

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