I have a case type to perform new user registration in constellation. where in constellation I can call case creation for this case type, I mean the login screen allowing to open this case type for any anonymous user.

Before constellation we used to customize web-login html from there we used to call case type as mentioned in this link -New User Registration Case Type on Login Screen

I have an idea to call DX API for case creation. But will I call this in webembed for users?

Any help in this regard would be appreciated.