Yes, WhatsApp, FaceTime, and other video/voice calling apps work perfectly fine in New Zealand over a data connection.
New Zealand has no restrictions on Voice over IP (VoIP) services, so you can freely use your preferred communication apps to stay in touch with friends and family. Whether you're making video calls or just quick voice messages, these services operate normally as long as you have an active data connection.
Your eSIM will provide this connection by automatically connecting to the strongest available major mobile network in New Zealand. The exact network your eSIM connects to can vary by plan, but all major networks support these services without issue. Just ensure you have sufficient data on your eSIM plan for extensive calls, as video calls can consume data quickly.