Can anyone help me or give me some guidance with Firebase Authentication?

I am developing an application with login and registration connected to a Firebase Auth database, but I cannot connect the app with Firebase Auth and I cannot find an extension that works for me. Will there be someone who can help me please? I have been stuck with this for days. I have already looked. Many tutorials on the internet, forums and so on, but nothing works for me. Attached is a screenshot of the blocks I use.

You do not appear to be doing anything if registration is successful ?

Why have all those checks, just return the error message to the user.

This method works for me every time: