This is a pretty common pattern for applications that support using multiple identity providers via protocols like OAuth or SAML. The site looks up the supplie

This is a pretty common pattern for applications that support using multiple identity providers via protocols like OAuth or SAML. The site looks up the supplied email and decides where to send the user - if they have a password, ask them for it; otherwise send them to their identity provider to authenticate and sign them in at the end of that process. This does leak a little bit of information about users - a third-party could observe whether "bob@megacorp.co" gets redirected to Megacorp's SAML server or gets a password prompt.