please note:
wppizza has nothing to do with woocommerce (or any other wordpress ecommerce plugin for that matter).

although you should be able to use wppizza and woocommerce (or any other wordpress plugin) happily alongside each other, the do not talk to each other.

therefore – for the avoidance of doubt – you cannot use any of woocommerce’s gateways or checkout and/or cart functionality for wppizza , nor use any wppizza extensions/gateways for woocommerce.

they work totally independently of each other.

i.e
woocommerce gateways, plugins and extensions work with woocommerce only

wppizza gateways, plugins and extensions work with wppizza only

Furthermore, if you are using both, they will have their own checkout process