Master Nan can go on at length at times, but I would absolutely recommend reading the entire thing. Much about stuff not asked about, but some very good information about the foot channels and also some interesting exercises to help facilitate it. But to truly "breathe that deeply" it all begins with the bottom of the diaphragm, the crus of each leaflet attaching at the anterior of the spine. Trace from there to psoas to femur and you see the kidney sinew channel as I described in one of the grounding vs rooting posts around here. Perfect thing to be doing while in zhan zhuang
As far as I can tell the turtle breathing is referencing just the deep abdominal motion - that's all that is left after the other parts of the breath have been sufficiently smooth. Cant feel your breath at that point. Hibernation is a similar concept, its just that there have been different people describing these things over the years - you have to have all of the physical mechanisms timed well so that the energetic culminations of each part of breath will coherently come together producing higher amplitude energy potentials and continue reducing and attenuating aspects that are not absolutely necessary; streamline the entire process. You've read a lot of these keys from me before - I'm trying to amass all of my writing on this and make it into one coherent collection, since I've written in bits so often. I will share it when I'm done, whenever that might be
Even in mildly complex systems, any outcome is the wrong thing to target, with the process being where the focus should be.