Check if user exists from login page

In the login page I want to hide the “login” button if the user’s “mail” does not exist in the database and that this returns a message as “user not found”.
But when entering an email from a user that does exist, the “login button” appears

I had that condition on the button, but it stopped working

This approach is not recommended now with a new price policy.
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@Eugene_West can you attach the exact link for the user login isssues, (do a search for user) please.