creating a registration system with CI4, and why is CI "better"?

If your on a live server then you should be able to install them from the server control panel like CPanel.

I run on a dedicated server with Plesk 18 and console.  PHP 7.3 is installed and all my sites use it.  But for some reason, the OS itself (Ubuntu 16.04) has a "default" PHP of 7.0.33 installed, hence the issue....

You should stop trying to use composer.

Your shared hosts seems to have all CI4 requires, so go on your website and do it all manually.

Just download the source of Myth:Auth, put the files in your CI4 application (in the right paths), modify the configurations to setup your own app.
I personally have not yet tried Myth:Auth with composer, I needed to do it manually.