I am having the same problem & error message when trying to run first pay for new year, for period 27-Jun to 03-Jul.
Also, I finalised pays for 2020-21 in the Payroll Reporting Centre on 02-July, and subsequently, on 05-July, reviewing the EOFY Finalisation Screen for 2020-21, all employees remain ticked as finalised. Employees have checked their MyGov Inboxes, and there is no message from the ATO that their Income Statement is available. Is their a problem with the MYOB AccountRight / ATO interface, or is it just a matter to waiting?