Use the Primer GitHub App for auth instead of the GPR_AUTH_TOKEN_SHARED

[camertron]

What are you trying to accomplish?

This PR replaces usage of the GPR_AUTH_TOKEN_SHARED PAT with a token obtained through the Primer GitHub App in several CI scenarios.

Fixes https://github.com/github/primer/issues/2582

Can these changes ship as is?

• Yes, this PR does not depend on additional changes. 🚢

[changeset-bot]

⚠️ No Changeset found

Latest commit: f602fa1

Merging this PR will not cause a version bump for any packages. If these changes should not result in a new version, you're good to go. If these changes should result in a version bump, you need to add a changeset.

This PR includes no changesets

When changesets are added to this PR, you'll see the packages that this PR includes changesets for and the associated semver types

Click here to learn what changesets are, and how to add one.

Click here if you're a maintainer who wants to add a changeset to this PR