From what I understand from Information I read on different sources , That's Auckland offices can't run of full capacity due to lockdown level 3 , so therefore paper applications in Auckland will be slower to process, because some part of their system need to be access physically to complete process, still some work can be done remotely but can't be completed  

Online Applications it can be processed from any DIA office, so my guess now that Auckland officers are processing some part of online applications when they are WFH , then transfer applications to another officer in Welly to complete application , maybe that's why we are seeing currently faster online processing.  

I am waiting for this request to be answer https://fyi.org.nz/request/16664-citizenship-paper-applications#incoming-64216 , hopefully tomorrow to give us more idea about paper applications.