AFAIK that email is only sent after someone attempts to login with the correct email and password provided. I'm assuming that your password is randomly generated and unique to Discord (so not in another website's data breach), so that leaves in my view:

1. Your password manager itself was breached and your password was compromised through that (probably unlikely, and the password itself should be encrypted anyway)
2. Your device has malware on it that compromised the password (unlikely, since (a) it'd have the same IP as you, so the location would be the same and therefore no email; (b) it would just steal the session token stored on the device rather than login)

Neither of which really explain what's happening, though.

You could attempt to enable 2FA on your Discord account. Discord won't do email verification anymore if you've got 2FA enabled.