I have a quite adequate knowledge of neuroethology. I don't know what Jaynes is on about, to be fair, but if there isn't a big section of the book saying, "And here is why these hundredsof studies all pointing in this direction are in fact wrong, and as a bonus, the logic we use doesn't lead us to become solipsists," then I'm not sure it's worth my time regarding the answer to this question.

It might be worth my time otherwise, but not for this.

If you want to define a particular, different type of empathy, where there's a huge input from internal narrative, sure, that would arise along with the internal narrative. We are rich with narrative: we have narratives about why we're walking, about why the loud noise made us jump, about why we like this ice cream, and so on. If you manipulate people's choices, they'll still come up with a narrative explaining why they chose it.

It doesn't follow that social animals, which otherwise display all the characteristic behaviors that we would presume to assign to empathy if we observed in humans, don't have empathy. They probably don't have our obsessive narrativization.

And the evidence is that animals plan a good deal. See, for instance, https://www.sciencedirect.com/science/article/pii/S2589004221001632.