Whatever the internet tells you about what is "standard"... as someone who has spent his life in New Zealand, I can assure you the majority of under-30s usually use "zee". "Zed" is on its way out.

It probably started with the popularity things like Sesame Street and Dragon Ball Z (Dragon Ball Zee).

However, interestingly, the one time everyone uses "zed" is when we acronymise the country name -- NZ, or N-Zed.