Just to give everyone a data point and update to my situation, I called air new zealand directly to the new zealand number and after a 15-min hold, a very friendly and helpful agent picked up my call. I explained my problems, she asked a few questions to understand why I did not board the flight from PPT to AKL and why I missed the AKL-SIN leg. I explained to her that I was told at check-in that I could not transit in Auckland due to NZ govt policy, etc. Long story short, she agreed that I should get a refund for the AKL-SIN part (it was paid Premium Economy and it was refundable ticket), she said it will be processed in 2 weeks time. As for the PPT to AKL that my friend booked for all of us, she also agreed to refund this but it will take longer to process, up to 8 weeks. All in all, she was very helpful and efficient and professional.