Yes the PlayStation Network is down, meaning PSN and all of its services like the store are inaccessible on the PS4 and PS5 due to the outage.

PlayStation Network went down for PS4 and PS5 users, impacting just about every facet of PSN from account management to ...

The outage began Friday evening, and account management, gaming and social, PlayStation Video, PlayStation Store, and the PlayStation Direct website were all dealing with issues, ...