DIAGNOSIS This is almost always a Wi-Fi setup issue. The oven's wireless module only connects to 2.4 GHz networks, not 5 GHz. If your router broadcasts both on the same name (SSID), or you have a mesh system, the oven can get confused.
FIX You need to guide the oven to the 2.4 GHz signal. 1) On your phone, go to Wi-Fi settings and temporarily forget your home network. 2) Open the Breville app and start the device setup process. 3) When it asks you to choose a network, look for your network name that explicitly says "2.4GHz" or has a separate, dedicated 2.4 GHz SSID (you might need to log into your router to create one). 4) Complete setup with that 2.4 GHz network. After it's paired, you can reconnect your phone to your main network.
IF THAT DIDN'T WORK The oven's Wi-Fi module might need a hard reset. With the oven plugged in and on, hold the "A" and "C" buttons on the control panel simultaneously for 5 seconds until the Wi-Fi icon blinks rapidly. This clears its network memory. Then try the setup process from scratch.
HEADS UP The app connectivity is for remote monitoring and pre-heating only. You can't start a cooking cycle from the app for safety reasons, so don't expect full remote control.