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/org/config.el

@@ -532,7 +532,7 @@ relative to `org-directory', unless it is an absolute path."
             '("wolfram"     . "https://wolframalpha.com/input/?i=%s")
             '("doom"        . "https://github.com/hlissner/doom-emacs/%s")
             `("emacsdir"    . ,(doom-path doom-emacs-dir "%s"))
-            `("doomdir"     . ,(doom-path doom-private-dir "%s")))
+            `("doomdir"     . ,(doom-path doom-user-dir "%s")))
 
   (+org-define-basic-link "org" 'org-directory)
   (+org-define-basic-link "doom" 'doom-emacs-dir)