Answer

The requirement that one’s animal rest is a prohibition, but not punishable by stoning, karet, or a sin-offering like the prohibited labors themselves.
It seems to me that the category of unintentional violation is relevant here on the part of the person, of course, like any other prohibition. On the part of the animal, unintentionality has no meaning. Does it know that it is carrying from a private domain to a public domain? Or that this is a private domain and that is a public domain? Or that there is such a prohibition? What would unintentionality even mean here? Only in tort law do we find intent to cause damage with an animal (the primary category of goring), but even there the meaning is not intentionality in the human sense, but an act done in order to cause damage and not for some other purpose or in the course of its normal walking. The intent there is not a parameter of culpability, but a definition of the damaging category of goring.