Hi korti11,
This is an expected behavior. There is a limitation of workflow: An action in a workflow run can’t trigger a new workflow run. You can see this prompt in https://help.github.com/en/actions/automating-your-workflow-with-github-actions/events-that-trigger-workflows#about-workflow-events.
When you use GITHUB_TOKEN in your actions, all of the interactions with the repository are on behalf of the Github-actions bot. The operations act by Github-actions bot
cannot trigger a new workflow.
I would suggest you use your own PAT when add labels to an issue.
Store your PAT in secrets and use ${{ secrets.PAT } in your actions.

Then you can see it is you who added a label in the issue. This will trigger the other workflow which is configured:
on:
issues:
types: [labeled]