DIAGNOSIS The Linksys app is probably trying to connect via Bluetooth for setup, but your phone's permissions or the router's Bluetooth radio is interfering. Yeah, this one's common.
FIX First, force quit the Linksys app and restart it. On your phone, go to Settings > Apps > Linksys and make sure Location permissions are enabled (the app uses this for Bluetooth discovery). If it's still stuck, the nuclear option is to set it up via a web browser. Connect a laptop directly to the router with an Ethernet cable, open a browser, and go to http://linksyssmartwifi.com. The web interface should pop right up and guide you through setup without the app.
IF THAT DIDN'T WORK Make sure you're not connected to a VPN or ad-blocker on your phone, as those can block local discovery. Also, try turning your phone's Bluetooth off and on again to refresh the radio.
HEADS UP If you use the web method, you can still manage the router with the app later. Once it's fully configured and broadcasting Wi-Fi, the app should connect to it normally over your new network.