Hello and welcome.
I'm afraid there isn't an answer for your question. The COs have to check all of a number of matters for each applicant, and tick them off as being satisfactory, but there isn't a set order for them to do this in. Therefore, you can't draw any conclusions as to how far through the procedure your case is when you hear of any particular item being checked out.
Also, all that a CO needs to know about a medical is that it has been passed as ASH (acceptable standard of health) - they don't investigate it themself. Each medical will be checked in the first place (and this is triggered when your application goes into INZ, with the link to your eMedical) by computer. The computer will pick up any abnormalities noted by the examining doctor, and medications mentioned, but alongside that, we think, from other people's experience, that there are probably certain keywords (for instance, some past condition which was treated and cured some time ago) which can flag the need for a look by a human being. If that happened, and the first person to check felt there was need for an expert to consider it, that is when the case would be referred to an MA (Medical Assessor). MAs have the duty of understanding an applicant's state of health, and have the power to require extra tests and/or doctors' reports until the point when they can clearly see that s/he will not cost the NZ Health Service too much for care and/or treatment. It sounds as though this is what may have happened in your case. Messages from the MA are passed to the applicant through INZ (by a clerk if you don't have a CO yet), not directly, but that is separate from processing your application.
Meantime, when your case was lodged it will have been looked over by clerks, making sure, without doing any fact-checking themselves, that it APPEARS from what you have said about yourself and your situation, that the evidence you have supplied is enough (so, that this is a complete application), then it will have been added to the date-order queue waiting to be allocated to a CO for processing. COs each have an allocation of cases that they work in rotation (so, they send out queries on one case, then don't just sit waiting, but work on the next, and the next, and so on, with each file going to the back of their work pile and working its way round to its next turn for the CO's attention, when s/he will see what replies have come in and whether they can tick off some item, or if more questions need asking, round and round till all the boxes are ticked and s/he can recommend an outcome). When a CO finishes some cases and has room for more, s/he takes the next ones from the front of the date-order queue, and at that point only you have active verification of your evidence starting. And your CO will only need to tick off that your medical is ASH, i.e. the final outcome of the eMedical, plus referral to the MA if that was necessary.
So from all the above, you can see that getting the medical query is no clue to where your case might be in the date-order queue, or with a CO. If you phone INZ, the call-answerer
may be able to tell you if you have a CO yet (depending on what has been entered in the computer), but s/he won't be able to say how much longer processing will take, as, after the queuing, every case is different and dealt with individually.
If I were in your place, I would think it likely that I would need a partner-sponsored work visa.