From Home Assistant to SmartThings?

In the past, people have used either Ifttt or Alexa as a means of smartthings integration with the gogogate. Have you tried either of those?

It’s the same method as any Wi-Fi device not on the official compatibility list:

FAQ: WIFI Devices in ST? How can I integrate a WiFi or Bluetooth device that isn’t listed in the SmartThings app?