I consider the possibility raised by cardinal mario grech last year that the final document of the synod be sent first to dioceses around the world (so that they can draw their own conclusions) and only then to the pope; I believe that in this way the false church would be born of bishops and lay people who freely chose to abdicate Catholic doctrine; and the false church would not be officially institutionalized but would compete for space in our dioceses with the true one; in that scenario predicted in Garanbadal of bishops against bishops and cardinals against cardinals. "He also suggested that the assembly might decide not to submit its final document immediately to the Pope, but to send it instead to dioceses around the world. “In this case, the final document would reach the Bishop of Rome, who has always been recognized by all as the one who issues the decrees established by councils and synods, already accompanied by the consensus of all the Churches,” he said." https://www.ncregister.com/cna/pope-francis-path-to-2023-synod-on-synodality-faces-3-risks
I do think something like what you described will play out. A schism will develop for sure. And "soon." A few bishops will be on the traditional side (hermeneutic of continuity). Many bishops on the side of synodality (hermeneutic of rupture). The physical church buildings will go to the side of rupture eventually because of legal reasons. The "false church" as it exists right now is a state of mind. Those who believe in "the church of continual reform" are members of "the false church," in their minds. In the material world, at the moment, false (rupture) and true (continuity) exist in the same physical buildings and hierarchical apparatus. It is the Parable of the Wheat and the Tares.
I think this pontificate tends to hand over controversial decisions (reforms) into the hands of the local Churches in such a way that it does not use the power of the keys (manifested to the universal church) in other words it is exploring as much as possible the ways in which the Church can err, for example in the context of local Churches and in the free interpretation of documents of the magisterium (something that has been developing since Vatican II).
