Fix dependencies between rust-mode implementations

"rust-prog-mode.el" and "rust-mode-treesitter.el" provide competing
implementations of `rust-mode'.  Both implementations depend on code
in "rust-mode.el", and thus must require that.

Doing that is complicated by the fact that "rust-mode.el" loads one
of these libraries, depending on `rust-mode-treesitter-derive's value.

Address this conflict by:

1. Requiring feature `rust-mode' in the two libraries that implement the
   `rust-mode' major-mode and that use things defined in "rust-mode.el".

2. Moving the require forms for these two libraries in "rust-mode.el",
   below the `provide' form for `rust-mode'.

rust-mode-treesitter.el

@@ -5,12 +5,13 @@
 
 ;;; Code:
 
+(require 'rust-mode)
+
+;; Do not compile or load on Emacs releases that don't support
+;; this.  See https://github.com/rust-lang/rust-mode/issues/520.
 (when (version<= "29.1" emacs-version)
-  ;; We have the when macro because of
-  ;; https://github.com/rust-lang/rust-mode/issues/520
   (require 'treesit)
   (require 'rust-ts-mode)
-  (require 'rust-common)
 
   (define-derived-mode rust-mode rust-ts-mode "Rust"
     "Major mode for Rust code.

rust-mode.el

@@ -71,17 +71,19 @@ instead of `prog-mode'. This option requires emacs29+."
     map)
   "Keymap for Rust major mode.")
 
-(if (and (version<= "29.1" emacs-version) rust-mode-treesitter-derive)
-    (require 'rust-mode-treesitter)
-  (require 'rust-prog-mode))
-
 ;;;###autoload
 (autoload 'rust-mode "rust-mode" "Major mode for Rust code." t)
 
 ;;;###autoload
 (add-to-list 'auto-mode-alist '("\\.rs\\'" . rust-mode))
 
 (provide 'rust-mode)
+
+(if (and rust-mode-treesitter-derive
+         (version<= "29.1" emacs-version))
+    (require 'rust-mode-treesitter)
+  (require 'rust-prog-mode))
+
 (require 'rust-utils)
 
 ;;; rust-mode.el ends here

rust-prog-mode.el

@@ -4,7 +4,8 @@
 ;; rust-mode code deriving from prog-mode instead of rust-ts-mode
 
 ;;; Code:
-(require 'rust-common)
+
+(require 'rust-mode)
 
 (defvar electric-pair-inhibit-predicate)
 (defvar electric-pair-skip-self)