[CI] BK Integration tests: Run non-sudo tests

[pazone]

What does this PR do?

Adds non-sudo tests to the new Buildkite integration tests

Why is it important?

Checklist

• My code follows the style guidelines of this project
• I have commented my code, particularly in hard-to-understand areas
• I have made corresponding changes to the documentation
• I have made corresponding change to the default configuration files
• I have added tests that prove my fix is effective or that my feature works
• I have added an entry in ./changelog/fragments using the changelog tool
• I have added an integration test or an E2E test

Disruptive User Impact

How to test this PR locally

Related issues

Questions to ask yourself

• How are we going to support this in production?
• How are we going to measure its adoption?
• How are we going to debug this?
• What are the metrics I should take care of?
• ...

[mergify]

This pull request is now in conflicts. Could you fix it? 🙏
To fixup this pull request, you can check out it locally. See documentation: https://help.github.com/articles/checking-out-pull-requests-locally/

git fetch upstream
git checkout -b ci_bk_non_sudo_tests upstream/ci_bk_non_sudo_tests
git merge upstream/main
git push upstream ci_bk_non_sudo_tests