Your sending carries on while you sort this out.
- Warming, DNS checks and IP monitoring run on their own schedule, not on yours.
- Nothing pauses because nobody is signed in.
- Setting a new password signs out every other device, which is the point if you are here because you think someone else got in.
If the address has no account, no email is sent and we do not say so here. Confirming which addresses are customers is not something a login page should do.