No network requests happen when you click generate. The key is created and encoded entirely in this tab's memory using tweetnacl (loaded once from cdnjs) and the browser's own random number generator. Nothing is sent anywhere — closing or refreshing this tab destroys the key permanently, so copy or download it right away.
ssh-keygen -p -f path/to/key. Treat the
downloaded private key file like a password — store it somewhere only you control, and delete it
from Downloads once it's moved.