I wasn't aware that there are Habsburgs who are Traditional Catholics. My ancestors used to know them.
The young woman who will be an Archduchess (someone told me she is already?) is actually a pro-life advocate who has lived in DC for a while. I saw her speak back in 2010. I've been told she used to attend the SSPX chapel in Cincinnati, but she was not there when I was there, at least I didn't recognize her. Before that I'm pretty sure I saw her once working at an ice cream shop several years ago. I saw her at mass at the indult parish the Sunday after Thanksgiving and on Christmas. One of the girl's in John Vennari's video is her friend, is her age and was at the same college as her. She was in our Legion of Mary meeting, and came back from DC to speak of her visit with her. The engaged (married?) girl's maternal grandfather lived right next to my Catholic grade school parish. Her aunt lived right across the street when I was a small child, I used to play with her cousins. Although that would have been before she was born.
I met the girl in that video not long after it was made, in 2009.
That is the extent of my personal knowledge of this.
I have no knowledge as to how traditional any of the Habsburgs are.
I believe this one is related to the Grand Duke of Luxembourg, who was stripped of any actual power a few years ago when he refused to accept a euthanasia law.