US -NZ Immigrant- IRD tax on US Holdings?

Hi,
My Kiwi wife and I came to NZ Jan 2020 on a planned short term family visit and got caught in the COVID lock-down. here July 2021. I was just granted a NZ Residency Visa (not Permanent) . I heard that NZ IRD will grant us a 4 year period before starting to tax our US income , but I am confused about if they will also attempt to tax our US stock holdings in our US Schwab accounts after the tax relief window.
I have tried to read the NZ IRD website , but cannot interpret it well.
Can anyone suggest websites where I could go to find information, or online groups where people discuss such experiences?
I thought I hear that NZ IRD will tax not just income created from selling positions, but also 5% p.a. for the holdings in all accounts.
Seems impossible that they would ,but the impact on us would be huge, as we are just retiring and most of our holdings are in our Schwab and Vanguard accounts.
Thanks in advance.