Always use a hidden email service, you cannot trust the LLM or inference provider to secure the email address in this context. If they don’t have the email address, they can’t leak it.
I never give a provider my actual email address, I recommend others do the same. Otherwise, it’s just a matter of time until it is leaked or otherwise part of a data breach.
If you let the LLM see git commands, they have whatever email you use to sign commits.