She was granted immunity for testimony. Had she testified, instead of willfully ignoring the court, she would not have been held in contempt.
Either way, with immunity granted, there's no Fifth Amendment peril there.
She claimed a lot of legally nonsensical things on stand so I'm not sure any of it passed any scrutiny. It certainly didn't with the judge.
https://www.washingtonpost.com/local/public-safety/chelsea-m...