Auckland is expensive partially due to immigration. Auckland region[1]:

  The proportion of people born overseas was 41.0%, compared with 27.1% nationally.

When over 1/3 of the population is immigrants that causes housing demand.

Fabulous "Upzoning New Zealand" article on NZ housing policy: https://worksinprogress.co/issue/upzoning-new-zealand/ which mentions Auckland increased housing supply by 4% from 2016 to 2021. It also mentions large house supply growth in Christchurch and how house prices have been going up in Christchurch despite that.

[1] https://en.wikipedia.org/wiki/Auckland_Region

Every country that does has this housing problem.