Firebase auth clients can automatically send an email to a user when they try to sign in using password-less signin. For example, all you have to do in the android client is auth.sendSignInLinkToEmail(email, actionCodeSettings) and the firebase servers take care of everything. That means that there's already an email template, SMTP configuration, etc to be able to send that email.
How can one tap into that infrastructure but from a backend? all I find in the admin sdk is how to generate the sign-in link but that would force one to set up a service to send the email, deal with templates and localization and other things that give you extra flexibility but that are not necessary if the existing mechanism works well for you