I'm aware of the Vism. interpretation of kaya as whole "body of breath" for step 3 anapana. You are probably aware of the schools of Theravada that interpret step 3 as whole anatomical body. I'm not here to debate which interpretation is correct, believe whatever works for you. Whatever interpretation people believe, just for your reference consider the Chinese Agama version of step 3 anapana clearly, unambiguously, and with copious similes asserts the "whole anatomical body" interpretation.
Regarding the statement :
Kāyesu kāyaññatarāhaṃ, bhikkhave, evaṃ vadāmi yadidaṃ – assāsapassāsā.
I tell you, monks, that this — the in-&-out breath — is classed as a body among bodies.
I take that to mean step 1 and 2 of anapana, (clear knowing of long/short in/out breath), count as a physical "kaaya" to justify it's place in the first tetrad of anapanasati 16 steps and first tetrad satipatthana, kayaanupassi.
Also, looking at MN 119, (thanissaro trans. from ATI)
"Furthermore, quite withdrawn from sensuality, withdrawn from unskillful mental qualities, he enters & remains in the first jhana: rapture & pleasure born from withdrawal, accompanied by directed thought & evaluation. He permeates & pervades, suffuses & fills this very body with the rapture & pleasure born from withdrawal. Just as if a skilled bathman ...
For the "whole anatomical body", that sutta passage makes sense. If we go with "body of breath", how exactly do you permeate, pervade, suffuse and fill "body of breath" with pleasure and rapture? Does "body of breath" have a nervous system that sends signals of piti and sukha to the brain?
Note all 4 jhana similes (corresponding to 4 jhaanas) use that statement "He permeates & pervades, suffuses & fills this very body with the rapture & pleasure born of composure"
Also, the canonical formula for 3rd jhana states "sukhanca kayena patisamvedi". Kaya as anatomical body would seem to be the most natural interpretation.