They do not need to hide the backdoor's existences though

Just add a 'USGOV BACKDOOR' tab and password/encrypt it or whatever the fuck. It doesn't need to be a real control panel or anything other than trivial options (a grayed-out unchangeable toggle box that says 'Enable backdoor', for instance). I'm not the guy to provide you UI tips.

Let users understand it's there without relying on security-through-obscurity. Disallow any temptation to use StO and ensure users are fully informed of the government's firm and fatherly hand.

Yes, I know that the GUI/man page information are not 'the backdoor'. It is also not actually any functionality for the software you're using. It is function through abstracted symbols.

Protest via abstracted symbolism - visible and immutable vulnerability.