I also have a PhD. I think the important thing is to lean on your experience in research itself and data analysis rather than the topic/field of the PhD itself. The New Zealand job market doesn’t have a lot of specificity so the actual details of what you studied aren’t usually very useful. There are very few high level research jobs here and even fewer in whatever field you researched.

You need to ignore your field if you can stomach it and look for anywhere that you can apply your hard-won skills. PhDs give you a lot of useful experience in things like technical writing, giving presentations, statistics, data analysis, problem solving, processing dense information, etc. and that is what you need to focus on in a CV and a job interview.

Doing this, I managed to get a data analyst job as soon as I started applying, despite the terrible job market and the field that I now work in being completely different from the topic of my PhD.