I don’t know how to do it from the client’s computer, but since I know you’re using this for Sagittarius, just pass the string {{IP}} as the IP when you create a new server, and the App Engine app will automatically detect your computer’s IP for you.
And actually, I discovered while making Sag that it’s near-impossible for a computer to “know” its own IP without sending a round-trip ping to a remote server. For example, the IP you see in command line or terminal is often just the local network IP (behind a router) or worse a mask. This IP will not work when trying to connect to a multiplayer game.