I, too, have been experiencing this issue for the past 12 hours. If I can get the app to open, however, after countless attempts, the games in my library are missing, or I can't launch any games. I've verified my ISP and any computer or graphical updates that could remotely be the cause and have had no luck. It seems the issue is random, as I've been able to access the EA App from a different computer on the same wifi connection with zero issues.
On the downed-sites reporting websites, not many, but a large portion of people are reporting the same issue with the EA App with login, server connection, or launching games in general.
Also, if it's relevant, for a brief moment last night, I was able to access the EA App with no issue, but the only game that could launch was the Sims 2 Legacy Collection, which then subsequently crashed.
Other notes: I do have mods for Sims 4, but nothing game-changing to prevent the game from opening, I have Restarted the App and used App Recovery multiple times, which usually leads to me back to being locked into the vicious 'Can't Connect to Servers' pop-ups cycle, and I've restarted my internet and computer numerous times.
Unfortunately, I haven't seen anything from EA mentioning this issue, and their Server Status page says everything is Online, so I guess it's just a waiting game... :/