Cycle touring in NZ is fantastic if you choose your route carefully.
A lot of the North Island is a bit too busy nowadays but there are still great routes through lovely country, such as the East Cape and the Wairarapa, logging trucks can be a bit of a nuisance in places.
The South Island is far better and most roads apart from State Highway 1 are relatively quiet except at weekends and in peak holiday season, Xmas/January.
Most main roads have a decent width of sealed shoulder, but it sometimes disappears at bridges etc.
I've cycle toured extensively throughout NZ, and lived there for a few years back around 2000, last time there was 9 years ago so probably some changes but not dramatic.
There's also now the NZ Cycle Trail project which links up off road routes the length of the country
https://www.nzcycletrail.com/