If the SBA denies a PPP loan application, who sends the notice of denial, the SBA or the bank through which the application was submitted? If it's the bank, do we have to include information on the steps for reconsideration from the SBA or can use our standard AA form?

You are the lender - the SBA just guarantees the loan. The only time SBA would deny a PPP application is if the borrower had either a delinquent or default status on a prior SBA loan. Otherwise, SBA’s application system would approve the application as soon as the lender submits it.