I used "service animal" because airlines are not required to accommodate any type of "animal that provides a service" in a seat that wasn't paid for. Whether it's a "service animal" or an "emotional support animal," airlines can't be compelled to accept the animal if it doesn't fit within the bounds of the seat that the owner paid for.
Having a disability doesn't mean that you get more seats for free. When it comes to the size of the animal and encroaching on other people's space, airlines treat ESANs and SVANs the same.