docs: update logger.md

[tsop14]

Description of your changes

Logger documentation update. Reading docs for the first time, this library looks great (looking forward to trying it out) but I believe a few of the log output examples are out of sync with the handler.ts code.

• Appending persistent additional log keys and values
  • example logs: add "aws_account_id" to highlighted text as this is also set in persistentLogAttributes
• Appending additional data to a single log item
  • example log 2: update message
  • example log 3 highlight "extra" property instead of "xray_trace_id"
• Logging errors
  • set log message as value passed to logger.error() and set error object message to Error message

How to verify this change

Run code in handler.ts and verify log output matches updated Example CloudWatch Logs excerpt

Related issues, RFCs

Issue number: #1049

PR status

Is this ready for review?: YES
Is it a breaking change?: NO

Checklist

• My changes meet the tenets criteria
• I have performed a self-review of my own code
• I have commented my code where necessary, particularly in areas that should be flagged with a TODO, or hard-to-understand areas
• I have made corresponding changes to the documentation
• I have made corresponding changes to the examples
• My changes generate no new warnings
• The code coverage hasn't decreased
• I have added tests that prove my change is effective and works
• New and existing unit tests pass locally and in Github Actions
• Any dependent changes have been merged and published in downstream module
• The PR title follows the conventional commit semantics

Breaking change checklist

• I have documented the migration process
• I have added, implemented necessary warnings (if it can live side by side)

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[saragerion]

Thanks so much @tsop14 for your kind words and taking the time to make this library better ❤️

Glad to have you as new first time contributor! 🚀

[dreamorosi]

Hi @tsop14 thank you for taking the time to open a PR in this repo, appreciate your time.

Leaving here the screenshots of the rendered docs for future reference of the changes:

[saragerion]

Note, the preview of the changes is visible here:
https://awslabs.github.io/aws-lambda-powertools-typescript/dev/core/logger/

It will be available in the "latest" version with the next release.