How to enable Full-Screen Mode in Settings Menu on my Mac?

Can you start by explaining which Settings you're talking about? I'm guessing you mean the System Settings (nee Preferences), but it isn't clear.

Assuming I'm on the right track, what makes you think the system settings warrant a full-screen app mode? Most of the sections there contain a few options that are optimized for the size of the window. Blowing the app up to full-screen would mostly just show you a carpet of grey, which isn't aesthetically pleasing to most people.

Simply put, Apple has Not Designed System Setting to appear as Full Screen.

You are welcome