I played with links using mklink vs a shortcut and here is what I found,
If I make a shortcut and place it in the default directory, it works ok for opening an existing project. If I create a new project without navigating to your desired directory, it will ignore the shortcut in the default path and create a new projects directory there and place your new project in it.
If I make a link using mklink, it works as expected. The path will still show the default C:\...... path but the new project will land in the directory you set up.
To prepare, if there are any projects in the default project directory, move them to where you want them. once that's done delete C:\users\public\documents\altium\projects, leave the altium directory.
from an admin command prompt,
mklink /D "C:\users\public\documents\altium\projects" "your\projects\directory"
I used "D:\circuitstudio\projects" on my system for example.
note the quotes and the slash type on the /D
mklink will respond with symbolic link created for { path data } if successful.
I think this works a little better than a shortcut.