No locules present. So cannot be Rhizopogon.
Scales support something like Endoptychum, but no stipe present.
REALLY need mature specimen for this one, I’m afraid. Keep checking, please?
The sectioned specimen does seem to have an oddly expanded sterile base, much wider on one side than the other. May still be an odd form of puffball as you originally suspected. Knowing what species of pine this is with could help as well. Maybe Monterey pine (Pinus radiata)? I believe this species was introduced widely to Australia and New Zealand both.