That distinction matters. Pausing ordering and hiding the menu solve different problems for a restaurant.
From a customer perspective, the menu should stay browseable with ordering clearly marked as unavailable until your restart time. If the current behavior hides it entirely, I would treat that as a visibility issue: repeat customers may think the menu moved, the business is closed, or the site is broken when they only wanted prices before calling.
As a workaround, I would keep one always-visible menu page for browsing and put the status message right at the top of it: online ordering is paused, call-in orders are accepted, and online ordering reopens at the specific time. Then make the same message visible anywhere a customer normally starts an order, so they do not hit a dead end.
If you are making the case for Square to bring the old behavior back, the strongest argument is that paused ordering should mean read-only menu, not hidden menu. Those states have very different impact on customers who use the online page as the live menu.
