The way I understand it in practice it is a combination of both. A group of men or women Catholics would approach the Church and ask to organize a community. They can organize freely, but the Church does not need to recognize them. If they are to get official recognition, they do need to submit to the Church's authority. In order to get recognition, they do need to be an organized and functioning community, and allow the Church time to decide to grant recognition. The other way religious groups form is to break off another previously established order, for some reason such as establishing themselves in another region.
so the final test will be
whether those Catholics whom the organization serves
care, respect, appreciate, want institutional conformance with
the institutional authorities of the Roman Catholic Church,
or
will those Catholics whom the organization serves continue to accept their service if approval of the Church does not come with it.
I guess.
(and many Catholics say one of the major errors of Protestantism is they are so divided - hmmmmm).
Seems the truth might be more that when Protestants “split” they don’t keep the institutional name/label of whom they split from, while all kinds of Leftist Catholics remain attending Catholic Churches while organizationally trading on the Catholic label while decidedly not conforming with many Catholic positions.
At least when some Anglicans started splitting over “same sex” unions it was honest. They didn’t try to brush the difference under the rug in the name of “unity” and for the pride and pretense of it.