Being logged out of iCloud web app and receiving AUTH_ERROR_INVALID_USR_TOKEN on devices

I started facing an error while logging in into iCloud.com website, few seconds after a successful login, I'm logged out from the app, it happens on any browser (even Safari from Mac) and after a password reset.

At the same time, I noticed an error when trying to enable mail on iCloud Mail on IOS receiving the message: AUTH_ERROR_INVALID_USR_TOKEN