I've been trying to perfect my runs recently but I've realized that PC and PSVR users don't need to do FNaF 2's withered Mode to unlock pizza party, on the quest version do I need to complete withered Mode or can I skip it as well and still unlock pizza party?

Really..? - I’d have to do some research on the matter since I don’t really know myself.

It is not necessary to beat Withered mode in FNAF 2 to unlock Pizza Party, thus not effecting the run. You can beat Night 5 and be done with that selection of levels. No, it is not needed on any platform or device for Pizza Party, so you don't need to do it for the run. Hope this helps!