If the bank is open for business on Saturday, but nothing hard post to accounts until Monday - is Saturday considered a business day for Reg E

What do you mean open for business?

2. Substantially all business functions. Substantially all business functions include both the public and the back-office operations of the institution. For example, if the offices of an institution are open on Saturdays for handling some consumer transactions (such as deposits, withdrawals, and other teller transactions), but not for performing internal functions (such as investigating account errors), then Saturday is not a business day for that institution. In this case, Saturday does not count toward the business-day standard set by the regulation for reporting lost or stolen access devices, resolving errors, etc.

Inherent Risk's text is actually from Reg E's OSC at 2(d)-2:

https://www.bankersonline.com/regulations/12-1005-002