refactor: deprecate doom-private-dir for doom-user-dir

- Deprecates the doom-private-dir variable in favor of doom-user-dir.
- Renames the pseudo category for the user's module: :private -> :user.
- Renames the doom-private-error error type to doom-user-error.

Emacs uses the term "user" to refer to the "things" in user space (e.g.
user-init-file, user-emacs-directory, user-mail-address, xdg-user-dirs,
package-user-dir, etc), and I'd like to be consistent with that. It also
has the nice side-effect of being slightly shorter. I also hope
'doom-user-error' will be less obtuse to beginners than
'doom-private-error'.

modules/lang/emacs-lisp/demos.org

@@ -386,7 +386,7 @@ Or to create aliases for functions that behave differently:
 ;;; Lets say we're in ~/.doom.d/config.el
 (load! "lisp/module")                  ; loads ~/.doom.d/lisp/module.el
 (load! "somefile" doom-emacs-dir)      ; loads ~/.emacs.d/somefile.el
-(load! "anotherfile" doom-private-dir) ; loads ~/.doom.d/anotherfile.el
+(load! "anotherfile" doom-user-dir)    ; loads ~/.doom.d/anotherfile.el
 
 ;; If you don't want a `load!' call to throw an error if the file doesn't exist:
 (load! "~/.maynotexist" nil t)