Same in New Zealand actually. As a longterm resident of Japan it would be cheaper to buy a brand new apartment in the middle of Tokyo than it would some damp hovel in Auckland.
The proportion of people born overseas was 41.0%, compared with 27.1% nationally.
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.