continue-on-error とプリインストールされているghコマンドを使えば簡単に出来る。

name: Test

on: push

concurrency:
  group: ${{ github.workflow }}-${{ github.ref }}
  cancel-in-progress: true

jobs:
  test:
    timeout-minutes: 8
    runs-on: ubuntu-latest
    steps:
      - uses: actions/checkout@v4
      - name: Test
        id: test
        run: |
          exit 1
        continue-on-error: true
      - name: Create issue
        run: |
          gh issue create --assignee "hrdtbs" --title "Issue report" --body "" --repo $GITHUB_REPOSITORY
        env:
          GH_TOKEN: ${{ secrets.GITHUB_TOKEN }}
        if: steps.test.outcome == 'failure'