Use trusted publishing approach to publish to NPM (PP-3299)

[tdilauro]

Description

• Updates the "release" GitHub Actions workflow to use the "trusted publisher" paradigm to publish this package to NPM.
• Updates the README to more accurately reflect the current release/publication process.

Note: This change depends on changes (already made) to the configuration for this project on NPM.

Motivation and Context

NPM deprecated and has now phased out long-lived tokens for publishing via CI. Trusted publishing is now the recommended approach.

[Jira PP-3299]

How Has This Been Tested?

This PR makes changes only to the GitHub Actions release/publication workflow and a README file. No updates are made to the actual package code.

Once this change is merged, we will need to perform a release to verify that it is working correctly.

Checklist:

• I have updated the documentation accordingly.
• All new and existing tests passed.

[jonathangreen]

🎉 looks great!

[jonathangreen]

Once this gets implemented everywhere, we should probably clean up the old token secret.