Fix mismatch between cookie field names in configuration schema and actual usage

[ishiyama0530]

There was a discrepancy between the cookie field names defined in the configuration schema and the ones actually used. As a result, the value specified in auth() was not being applied correctly.
This PR fixes the issue by aligning the field names to ensure proper behavior.

[jfromaniello]

Sorry for the delay! It looks good, is there a way you can sign the commit?
The org policy doesn't allow me to merge because the commit is not signed.
Github has some docs for helping the setup

• https://docs.github.com/en/authentication/managing-commit-signature-verification/generating-a-new-gpg-key
• https://docs.github.com/en/authentication/managing-commit-signature-verification/signing-commits

Thank you!

[ishiyama0530]

I’ve applied the settings. Could you check if working correctly?

[jfromaniello]

Thank you!!!

[github-actions]

🎉 This PR is included in version 1.2.1 🎉

The release is available on:

• npm package (@main dist-tag)
• GitHub release

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