describe key for menu-bar items from `menu-bar-open` calls

Question

Preface: I disabled menu-bar-mode and bound <mouse-3> to menu-bar-open, via (global-set-key [mouse-3] #'menu-bar-open)

With this configuration, how can I get help for menu-bar items?
(My ugly workaround now is to temporary enable menu-bar-mode and call help with that enabled)

Problem is: pressing C-h k and then mouse-3 brings description for menu-bar-open.
What I'd like to get instead, is the same describe-key behaviour as on C-<mouse2> menus.
This should be done in a way, which does not break on emacs updates (i.e: redefining describe-key seems to dangerous).

If there is no way to do above , how could I bind <mouse-3> to open the menu-bar and get the desired help functionality?

Edit: Solution from Tobias is not complete, it does not show local-menu and minor-mode-menus. Function mouse-menu-bar-map, which is called from menu-bar-open collects them all.

Edit2: [C-down-mouse-3] does what I expect, but I can't remap this with:

(global-set-key [mouse-3] (lookup-key (current-global-map) [C-down-mouse-3]))

Answer 1

The value of the variable facemenu-menu is bound to C-<mouse2> and that value is a sparse keymap.

Instead of binding #'menu-bar-open to <mouse-3> you can also bind the sparse keymap defining the menu bar to <mouse-3>:

EDIT: As indicated by jue t is better to receive the menu bar keymap from mouse-menu-bar-map than to use the value of (lookup-key [menu-bar]) because the menu bar is changed dynamically. menu-bar-update-hook cannot be used for reacting on dynamical changes of the menu bar since that hook is only run when the menu bar is switched on. But an advice for define-key does the job as far as I could test it up to now.

(defun my-menu-bar-update (&rest _ignore)
  "Update the [mouse-3] menu bar."
  (unless my-menu-bar-update-running
    (let ((my-menu-bar-update-running t))
      (global-set-key [mouse-3] (mouse-menu-bar-map)))))
(my-menu-bar-update)
(add-hook 'menu-bar-update-hook #'my-menu-bar-update)
(advice-add 'define-key :after #'my-menu-bar-update)