[chore] Only run final CI step if triggered by a "release"

[nwithan8]

Description

We recently added the ability to manually trigger the "publish via CI" process (it is also automatically triggered by cutting a new GitHub release).

The final step of the CI, however, anticipates the presence of variables that are only present when a release triggers the CI.

This PR adds logic to the CI process that will skip this step if triggered manually.

Testing

Pull Request Type

Please select the option(s) that are relevant to this PR.

• Bug fix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Breaking change (fix or feature that would cause existing functionality to not work as expected)
• Improvement (fixing a typo, updating readme, renaming a variable name, etc)