The CGO3 camera acts as WiFi hotspot, offers a network node and DHCP server. It sends out its SSID over 5GHz WiFi band. If the ST10 didn't receive a SSID that matches the expected format, the CGO3 will not appear in binding menu.
A good test you have already done is to check if the SSID appers in the list of your phone. If not as in your case the probability that the WiFi module is defect is very high. Another root cause of this effect is a bad WiFi antenna.
Question: What is the color of the front LED of the camera? If it remains white solid the camera stuck in initialization phase. This is a strong hint to defect WiFi module. If it starts to blink green (waiting on connection) then we should check antenna (plug / wiring).