[2023] Apex legends lost connection to xbox live and ea servers

Do you have any other peripherals currently plugged in, such as headphones, chargers, or a wireless dongle? Can you try disconnecting everything aside from the controller you're using to see if that makes a difference when trying to sign in?

Aside from that, I'd definitely suggest going through these troubleshooting steps, in particular flushing and/or changing your DNS to see if there's an improvement.