Folder redirection -- Prevent users from saving to desktop and C drive ?

as the title of the question
use GPO folder redirection redirecting user files
Documents, Desktop, favorites, start menu, appdada, downloads to the server you are backing up.
https://docs.microsoft.com/en-us/windows-server/storage/folder-redirection/deploy-folder-redirection

or anywhere on their C drive

As for this, you need to remove Administrator rights. No GPO will successfully block this, you can at best hide the drive.

The above two are the best way moving forward, GPO the Desktop folder redirection and hide the C:\

I do NOT give users "local admin" rights, but they can still SEE the C: drive

How can I "hide the C: drive" ?

Seeing is not an issue.
Commonly users do not have rghts to save n the C drive outside of temp, their profle and any foldr the admin adds and grants users access.
I am uncertain why you are so intensely focusing on this. Setting up folder redirection will go a long way.
Making it clear to users (who commonly decide to use shares, location where they have access for their own purposes)..

The issue with C: drive hidding is that the profile is there.
Look at user GPO ....
But to say it more directly, I think trying to go through extraordinary hoops where a simple advisory savin on the local system is susceptible to data loss.