Assign requested reviewers to pull requests

[alschmiedt]

Is your feature request related to a problem? Please describe.
We could not find an easy way to view all the requested reviews for a single person. This was leading to pull requests getting lost and forgotten about. We still want to use GitHub's auto assigner, however we also want to be assigned PRs.

Describe the solution you'd like
A GitHub action that will automatically assign the requested reviewers to the pull request.

Describe alternatives you've considered
There are GitHub actions available that will randomly assign a PR to a person (instead of requesting a review like GitHub). However, I could not find one that would take into account whether or not a developer had a status of busy or not.

Additional context

[rachel-fenichel]

The check script is now failing with "Resource not accessible by integration" (example run).

[cpcallen]

The check script is now failing with "Resource not accessible by integration" (example run).

This is the issue reported in #5659, though I am surprised to discover it applies to PRs from project contributors.