Action fails with "Not Found" when run in a merge queue

[twyatt]

To reproduce, created a sample project repo at: https://github.com/JuulLabs/merge-queue-test

Without merge queue enabled, github-action-required-labels works (JuulLabs/merge-queue-test#13) as expected:

GitHub Action run w/o merge queue

Run mheap/github-action-required-labels@v5
  with:
    mode: exactly
    count: 1
    labels: patch, minor, major, maintenance
    token: ***
    message: Label error. Requires {{errorString}} {{count}} of: {{ provided }}. Found: {{ applied }}
    add_comment: false

— https://github.com/JuulLabs/merge-queue-test/actions/runs/7154600875/job/19482310003

When merge queue is enabled, and github-action-required-labels runs from the queue, it fails (JuulLabs/merge-queue-test#14) with:

Run mheap/github-action-required-labels@v5
  with:
    mode: exactly
    count: 1
    labels: patch, minor, major, maintenance
    token: ***
    message: Label error. Requires {{errorString}} {{count}} of: {{ provided }}. Found: {{ applied }}
    add_comment: false
Error: Not Found

— https://github.com/JuulLabs/merge-queue-test/actions/runs/7154628159/job/19482369364