RE: A Catholic, yes.
What about those who were baptized catholic from infancy and then grew up to become reformed and evangelical ( see for instance Evangelist Luis Palau). Are they under the Vatican I anathema?
RE: pope has no secular power to compel obedience.
Again, let’s dispel with secular power, wars, troops, etc. Those are relics of ancient medieval times.
Does the Pope have real SPIRITUAL power to anathematize someone who believes in Jesus Christ but does not recognize that he is the Primate of the Christian church?
You are using a term as it it meant throwing thunderbolts from on high. The Council of Trent did what it did but it was in the midst of a civil war in the Church, against heretics who had the power to do great harm. Vatican I did what it did because the papacy was under assault from the secular powers of Europe and those even in the Church who wishes to destroy its power and influence. The threat to Church today does not come from the likes of Palau but from the secularists who are enemies of Christ, and the modernists within the Church.