I've never seen any filtering on P & K on the Air NZ site.

The Air NZ booking engine will purposely not display F class fares due to the restrictions that apply to these for international flights. The vast majority of Air NZ customers would not know that they could be saving huge $$$ in some situations by booking domestic flights by using the GAS website - even flights for travel days out can feature GAS F class fares that be hundreds of dollars cheaper than the Air NZ website.

Once you have forced the session token in your browser you can manually edit the browser URL to switch between both sites, ie if you have https://flightbookings.grabaseat.co....sk=-1885103625 you can manually edit this to https://flightbookings.airnewzealand...sk=-1885103625 (and then back again if you want) and this will switch between both sites and show F / non F availability.