[workflows] Update to use a GitHub app for our workflows, rather than using the GITHUB_TOKEN

This was a piece of feedback from @danieljurek for the nightly build workflow, but I think it's actually a universal concern and not just confined to nightly builds.

@danieljurek, am I correct on that? If not, I can scope this to just nightly builds.

Start with the nightly build workflow referenced in the issue, then inspect the other workflow definitions to determine whether the concern applies universally. Confirm the intended scope with the referenced feedback and consider the work complete when the applicable workflows use a GitHub App rather than GITHUB_TOKEN.

Written by the indexing model from the issue text.