tests: Run more upstream integration tests
    
    This requires a workaround for podman.service leaking processes on
    shutdown: https://github.com/containers/podman/issues/7021
    
    Some tests don't work in dist-git gating CI environment yet:
    testNotRunning, testRunImageSystem, testRunImageUser
    
    Also don't use run-tests yet, this requires
    https://github.com/cockpit-project/cockpit-podman/pull/437