Diagnosis
The setup process is failing to handshake with ecobee's servers. This is usually a firewall or DNS issue on your home network, or the servers are temporarily down.
How to Fix It
First, check the ecobee status page online (just search 'ecobee server status'). If it's green, the issue is local. Reboot your router and modem. Then, on the ecobee, go to Settings > Reset > Reset Registration. This clears its Wi-Fi and registration data. Start the setup in the app again from scratch.
If That Didn't Work
Some routers with aggressive security (like Netgear Armor or certain VPN settings) block the connection. Temporarily disable any 'Advanced Security', 'Intrusion Prevention', or 'VPN' features on your router during setup. You can usually turn them back on after.
Heads Up
The ecobee app setup is finicky. If it fails, force-close the app and restart it. Using a strong cellular signal (not Wi-Fi) on your phone for the setup process can sometimes help too.