He does indeed. I do not pretend that it is absolutely clear cut what is and what is not magisterial. Nobody has claimed that about infallibility, even since the beginning. But if you’re suggesting that by quoting himself a Pope’s teachings become part of the ordinary magisterium and so are covered by infallibility, I’m not sure I’d agree. Pope Honorius I presumably said things in public and wrote documents that quoted himself, but he was still judged a heretic by his successor Popes because he was a Monothelite. Pope John XXII preached a very serious error with regards to the Beatific Vision in a series of public sermons, but was later convinced to recant his errors.
None of these historic instances should be used as justification to attack this Pope or any other, but they serve to remind us that we can never abdicate our free will to exercise judgement in this life. There is an objective truth which we should choose if we are to call ourselves Christian, but that does not mean there is nothing stopping us from choosing another path. Free will, properly exercised, also means full responsibility.
We must also remember that in paragraph 3 of Amoris Laetitia Pope Francis says “I would make it clear that not all discussions of doctrinal, moral or pastoral issues need to be settled by interventions of the magisterium.”
I must also draw attention to your signature, which quite rightly says:
This religious submission of mind and will must be shown in a special way to the authentic Magisterium of the Roman Pontiff, even when he is not speaking ex cathedra; that is, it must be shown in such a way that his supreme Magisterium is acknowledged with reverence, the judgments made by him are sincerely adhered to, according to his manifest mind and will. His mind and will in the matter may be known either from the character of the documents, from his frequent repetition of the same doctrine, or from his manner of speaking. [Lumen gentium 25]
ewtn.com/holysee/pontiff/categories.asp
An Apostolic Exhortation is published to encourage the faithful to live in a particular manner (greater conversion to Christ) or to do something of virtue. An Exhortation does not have the ability to change Church teaching de fide. The dogmatic teachings of the Immaculate Conception and the Assumption could not be communicated to the Church as de fide in this form. For example, a post-synodal document offered to the Church which is typically a summary of a previous synod and hoping the faithful will do something helpful for the life of the church (e.g., the new evangelization, go to confession, rely on St Joseph, the moral life, preparation for a special event in the Christian life). This level is of ordinary teaching authority.
communio.stblogs.org/index.php/2013/11/what-is-an-apostolic-exhortation
It’s never a new doctrine but rather one that has been taught ubique, semper et ab omnibus (Latin for everywhere, always and by all). In other words, when the pope reinforces, reiterates, or restates the consistent teaching of his predecessors and of the bishops united with him around the world, that’s considered the Ordinary Magisterium and should be treated as infallible doctrine…
Since Vatican II, however, the content and context of the document determine the degree of authority and not just the type of papal document. If the pope intends to definitively teach the universal Church on a matter of faith or morals, then he is expressing his supreme authority as head of the Church.
When John Paul II issued his Apostolic Letter Ordinatio Sacerdotalis in 1994, he officially declared that the Catholic Church has no power to ordain women. Ordinatio Sacerdotalis was not an ex cathedra papal statement, but it’s part of the Ordinary Magisterium, and thus, according to the Prefect for the Sacred Congregation for the Doctrine of the Faith, the teaching is infallible…
Encyclicals are the routine, day-to-day, consistent teaching of the Ordinary Magisterium, which is equally infallible when it concerns faith and morals and reiterates the constant, consistent, and universal teaching of the popes and bishops. Their content requires religious submission of mind and will of faithful Catholics around the world.
So-called dissent from papal teaching in encyclicals isn’t part of Catholic belief. The Catholic faithful willfully conform to papal teaching and don’t dispute it.
dummies.com/religion/christianity/catholicism/what-are-extraordinary-magisterium-and-ordinary-magisterium