Finally I managed to set up CI for a Ruby Gem.
ere were some errors that stopped me from doing the regular steps.

A few days ago I sent a pull-request with a CI configuration to the RDF::KV module in Perl.
I was not very happy with the solution, but sent the pull-request anyway.
The author of the module was very responsive and soon pointed me to the step I missed, but also pointed at the Ruby port of rdf-kv.

Today finally I had the time to update the CI I wrote for the Perl version. (See the PR) and also to add the GitHub Actions configuration to the Ruby implementation and send the pull-request

name: CI

on:
  push:
  pull_request:
  workflow_dispatch:
  schedule:
    - cron: '42 5 * * *'

jobs:
  test:
    strategy:
      fail-fast: false
      matrix:
        ruby: [ '3.1' ]

    runs-on: ubuntu-latest
    name: Ruby ${{matrix.ruby}}
    container: ruby:${{matrix.ruby}}

    steps:
    - uses: actions/checkout@v3

    - name: Show Ruby Version
      run: ruby -v

    - name: Install dependencies
      run: bundle install

    - name: Run tests
      run: bundle exec rake

Conclusion

Maybe the earlier failures to set up CI for Ruby Gems wasn't even my fault. Maybe they really had failing tests.