エラーが出ている状態

.github/workflows/git-pr-release.yml

name: git-pr-release

on:
  push:
    branches:
      - develop

jobs:
  git-pr-release:
    runs-on: ubuntu-latest
    steps:
      - uses: actions/checkout@v4
        with:
          fetch-depth: 0 # git-pr-release needs the git histories
      - uses: actions/setup-ruby@v1
        with:
          ruby-version: 3.1
      - run: gem install --no-document git-pr-release -v "2.2.0"
      - run: git-pr-release --no-fetch
        env:
          TZ: Asia/Tokyo
          GIT_PR_RELEASE_TOKEN: ${{ secrets.GITHUB_TOKEN }}
          GIT_PR_RELEASE_BRANCH_PRODUCTION: main # 本番ブランチをを指定
          GIT_PR_RELEASE_BRANCH_STAGING: develop # ステージングのブランチを指定
          GIT_PR_RELEASE_TEMPLATE: .github/.git-pr-release

対応

以下を追加した

permissions:
  id-token: write
  contents: read
  pull-requests: write

動くやつ

.github/workflows/git-pr-release.yml

name: git-pr-release

on:
  push:
    branches:
      - develop

permissions:
  id-token: write
  contents: read
  pull-requests: write

jobs:
  git-pr-release:
    runs-on: ubuntu-latest
    steps:
      - uses: actions/checkout@v4
        with:
          fetch-depth: 0 # git-pr-release needs the git histories
      - uses: actions/setup-ruby@v1
        with:
          ruby-version: 3.1
      - run: gem install --no-document git-pr-release -v "2.2.0"
      - run: git-pr-release --no-fetch
        env:
          TZ: Asia/Tokyo
          GIT_PR_RELEASE_TOKEN: ${{ secrets.GITHUB_TOKEN }}
          GIT_PR_RELEASE_BRANCH_PRODUCTION: main # 本番ブランチをを指定
          GIT_PR_RELEASE_BRANCH_STAGING: develop # ステージングのブランチを指定
          GIT_PR_RELEASE_TEMPLATE: .github/.git-pr-release

これで動くことは動く