We have already partially answered this question, but I will duplicate it. Thanks КсH!
Excerpt from the documentation:

• If signUp() is called for an existing confirmed user:

  • When both Confirm email and Confirm phone (even when phone provider is disabled) are enabled in your project, an obfuscated/fake user object is returned.

  • When either Confirm email or Confirm phone (even when phone provider is disabled) is disabled, the error message, User already registered is returned.

  This means that if you need to receive the User already registered error, you should disable email confirmation in the supabase settings.