Every render of the prompt is fully stateless. Starship has no tracking, telemetry, and never calls home. :)
If you want to be 100% safe you could just monitor the process and see if it opens any internet connection but I am confident it is just a local program.
*threat
Why do people need all that information on their prompt? I understand showing the git status, but is it really necessary to know that your battery is discharging and you're currently using node v10.12.3 and elm v1.2.3 every single time you run a command in some directory?
I, for one, like to know what version of Node will be used when I'm jumping between projects, so I can know which features are available to me at runtime.
Eventually we'd like to include an interactive configuration tool to help folks find a configuration that meets their needs.