iCloud Private Relay service down for some users

According to Apple’s system status webpage and inconvenienced users on Twitter, Apple’s iCloud Private Relay service is currently down. The system status page also states it has been down since 1:40pm and at the time of writing is still not fixed.
Private Relay is a feature that encrypts all information your device leaves when browsing the web in Safari. The first relay is sent through a server owned by Apple and the second is through a third-party operator. This service was introduced at WWDC 2021 and is one of the many features of iCloud+.