You can either look at the code and see if it got sent or generate it offline using a tool like nostril etc.
I’m willing to bet that the key generation is done standard using a standard nostr library.
Discussion
I used rana to generate mine. It was made by #[5]
Nice.
And as you said. Looks like OP made up their mind on potential key exposure.
Another quick tip byrger is to get to the key generation screen and shut off all network connections. Most of these things work clientside and you can cut off any phone home stuff.