Maintenance: migrate package publishing to OIDC

[sthulb]

Summary

We should migrate package publishing to OIDC based tokens.

https://github.blog/changelog/2025-07-31-npm-trusted-publishing-with-oidc-is-generally-available/

Why is this needed?

To create a more secure Release pipeline.

Which area does this relate to?

Automation

Solution

No response

Acknowledgment

• [x] 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

Please react with 👍 and your use case to help us understand customer demand.

[dreamorosi]

We were able to successfully set this up in the powertools-mcp repository, so we can use the same pattern in this repo.

See aws-powertools/powertools-mcp#288 and aws-powertools/powertools-mcp#280 for reference.