I don’t think these are totipotent cells, as truly totipotent cells can only be derived from an embryo. These are stem cells that are deprogrammed to behave like totipotent cells. I am not sure of the technicalities, and am limited in my knowledge of genetics.
I am fairly sure that eggs are more than a convenient environment, they
are a necessary and essential part of reproduction. Without them, there can be no embryo, no fetus, and no unborn child. I think the entire point of this process is that the cells can be deprogrammed to act like the potentially beneficial embryonic stem cells, not that they have become or can become embryonic stem cells.
You have a mystical concept of cells. They are physical objects built from atoms and molecules, and can be tinkered with. If you want a cell to act like an embryonic cell, you just have to tinker with it until it has the same arrangement of atoms and molecules as a naturally occurring embryonic cell. Things are moving quickly in this field. Any details of how a given type of cell is built that are not known now soon will be.