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/autoload.el

@@ -247,7 +247,7 @@ https://emacs.stackexchange.com/questions/10230/how-to-indent-keywords-aligned"
 ;;;###autoload
 (defun +emacs-lisp-reduce-flycheck-errors-in-emacs-config-h ()
   "Remove `emacs-lisp-checkdoc' checker and reduce `emacs-lisp' checker
-verbosity when editing a file in `doom-private-dir' or `doom-emacs-dir'."
+verbosity when editing a file in `doom-user-dir' or `doom-emacs-dir'."
   (when (and (bound-and-true-p flycheck-mode)
              (eq major-mode 'emacs-lisp-mode)
              (or (not default-directory)