What should I write in the 'place of issue' field on my visa application if it states 'dia syd' on my passport?

Put “Australia” it’s what my partner and I did. We had “issued by” as the agency in our passports but many people said to use country and we did that and it worked. I read posts (use the search function in this group yourself) from people who got passports issued in a different country / city and that was listed in their passport and they wrote that (not country) and got their application cancelled

New Zealand has a department of Internal Affairs in Sydney? 🙃

Basically you applied for a new passport at the Embassy of New Zealand in Sydney, right?

I had a similar case since all of our passports were issued by various embassies. However, on the info page of our passports the issuing authority is clearly referred to as "EMBASSY OF XXX in YYY". That's what I wrote in the field and we got our visas.

Your case is somewhat different. This issue is debated, as John Macom pointed out, and there have been cancellations on this ground. If I were you, I would try to contact the embassy/consulate where I plan to submit my application.

put what’s on your passport. anything that is related to your passport has to match specifically your passport exactly. they can edit fields in your application except anything related to your passport.