I’m currently working on a book which will defend Pope Francis against the papal accusers. I’ve just finished the chapter defending Pope Honorius. I’ve read through the letters to Sergius, for which he was accused of heresy. There is no heresy in these letters, properly understood. It’s clear that the Pope never taught the error of Monophysitism, and never adhered to the error even privately. There are some assertions that he made which have been taken out of context. He is defended on these points by Saint Bellarmine, Saint Maximus, Pope John IV (his second successor), and Cardinal Manning of Vatican I.
There are no convincing cases of past Popes who have ever taught or committed heresy or apostasy or idolatry.