The public sin of manifest formal heresy is a kind of public defection from the Catholic Faith.
That's debatable.
Canon 188.4 speaks about the FACT of public defection and not the judgment of the Church for the loss of office to take place.
Person A says, (something heretical).
Person B says "Yeah, Person A publicly defected".
Person A says "No I didn't. I'm still Catholic."
Person C says, "What Person A said wasn't catholic but I don't think he meant to defect."
Catholic Knight says "We can all privately judge what Person A did."
Result - Protestant style, individualistic-minded chaos.
Once again, this goes back to your claim that one cannot judge the sin of heresy, for which claim you have refused to provide evidence.

The default position is this:
MAJOR - Canon law (i.e. Church Law) can only be administered/judged by Church authorities.
MINOR - Simple Priests and the Laity are not part of Church authority.
CONCLUSION - Simple Priests and the Laity cannot administer/judge using Canon Law.
You are the one that has to prove any catholic individual can judge heresy. The default position is a big, fat "No, you cannot." This applies to any court room, in any country, all across the globe. If you are not a lawyer, or trained in law, or a judge, you cannot take part in the legal process.