You will not find the Play Station 4 servers down anymore if you attempt to log into the console. Sony till now has not offered any kind of explanation for the hour-long outage which was on the 13th of June.
When the Play station 4 servers were down, they showed the error code WS-374037. Sony has no timeline on when the PlayStation Network will be back online. Everything that is official with the Network Service Status page for the network of PlayStation track has an angry red light next to it.
When the servers were down, players can play their games in offline mode. All the games which need some kind of license to renew will not be able to do and players will not be able to enjoy the game.
Sony will be skipping the E3 2019 because of their Network shutdown on the last day of the event. Sony is now working very hard to fix the issue which has been causing the whole server to crash multiple times. Now the status of Sony is under review and players cannot play games online.