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/tools/lsp/+lsp.el

@@ -45,7 +45,7 @@ Can be a list of backends; accepts any value `company-backends' accepts.")
         lsp-vetur-global-snippets-dir
         (expand-file-name
          "vetur" (or (bound-and-true-p +snippets-dir)
-                     (concat doom-private-dir "snippets/")))
+                     (concat doom-user-dir "snippets/")))
         lsp-xml-jar-file (expand-file-name "org.eclipse.lsp4xml-0.3.0-uber.jar" lsp-server-install-dir)
         lsp-groovy-server-file (expand-file-name "groovy-language-server-all.jar" lsp-server-install-dir))