I'm the author of one of the open source NZ vaccination passport libs. I'm pretty familiar with the specification and afaik I know theres no use of ZKP's. Its a fairly standard public/private key cryptography. Happy to be proven wrong though!
I'm indeed wrong, I had understood from a discussion with someone involved in the project that it was so :) Just had a chat with my buddies at mattr who corrected me :)
Here's the spec: https://nzcp.covid19.health.nz/ and our implementation https://github.com/vaxxnz/nzcp-js