The vax check will be built into the NSW app. Whether it returns a combined approval or a separate flag depends on the link between the internal applications. Either way I doubt anyone will be able see anything other than an approval flag. At the moment it seems that govt is happy to allow individual businesses to decide, but if this procedure is normalised and not opposed, it's possible that some rules might well be introduced to "protect" some businesses that might drag their feet.
Not sure how non smartphones and phone extant registrations will be handled! I have an idea but there are too many variables yet.
It's a clause in the current PHO that allows customer registration to be off line, produced on demand by the CHO. This is a loophole that will need to plugged to ensure system integrity. If this clause disappears it'll mean firm rules are on the way. Watch that space.