chore: fix for publish workflow asking npm cache

[himanshusinghs]

Description

At some point we added cache: npm to the publish workflow and that requires a repo checkout.
Since all the npm heavy work is already done by now, we don't need the cache anymore.

Checklist

• New tests and/or benchmarks are included
• Documentation is changed or added
• I have signed the MongoDB Contributor License Agreement (https://www.mongodb.com/legal/contributor-agreement)

Motivation and Context

• Bugfix
• New feature
• Dependency update
• Misc

Open Questions

Dependents

Types of changes

• Backport Needed
• Patch (non-breaking change which fixes an issue)
• Minor (non-breaking change which adds functionality)
• Major (fix or feature that would cause existing functionality to change)

[Copilot]

Pull Request Overview

This PR fixes an issue in the publish workflow where npm cache configuration was causing problems by requiring a repository checkout that wasn't available. The change removes the npm cache setting since the heavy npm operations have already been completed by this point in the workflow.

• Removes npm cache configuration from GitHub Actions workflow
• Eliminates dependency on repository checkout for npm caching
• Maintains workflow functionality while fixing the configuration issue

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