There is really no need for you to reply to my post. Whether kāya refers to the breath or the body in the third step of the Ānāpānasati Sutta is a relatively minor matter, which is unlikely to make much difference to anyone’s practice. I know people on both sides of this divide who have had success with mindfulness of breathing. I would suggest letting it be. If you do reply, I am unlikely to respond. I want to avoid spending so much time on matters of little practical importance.
What is important is the nature of the jhānas. I hope to get back to this later, but I can make no promise when that will be.