Affirm or deny:
The public sin of manifest formal heresy by its very nature separates the heretic from the Church.
Your insistenced upon a binary Yes or No drives the answer toward a false dichtomy.
I believe this to be true, though I object to your constant use of the world sin, as in public sin, since it can imply a judgment regarding the internal forum, which is not required.
Other than that, I hold the proposition to be true, and Pope Pius XII taught this.
Nevertheless, the Cajetan opinion and others have not been explicitly condemned, so one can hold them as a Catholic.
In addition, does a manifest heretic sepeparated from the Church lose office? And that too can be distunguished, where, for instance, the sedeprivationists hold that he loses office not
simpliciter, but
secundum quid, where he loses the ability to formally exercise the office (and Fr. Chazal would say the same with sedeimpoundism), but remains nevertheless in material possession of and with legal claim TO the office.
I also don't believe, however, that the question is even relevant, since the I hold to the "Siri Theory", where none of them have been legitimate popes after the election.
So the tactic of trying to force binary yes-no answers to questions that admit of various distinctions is an attempt to drive toward acceptance of your false dichotomy.