How to make `C-x 9` the same as `C-x 8 "`

Question

For typing german text with an english keyboard layout the binding C-x 8 " is very valuable. After typing it I can insert umlauts easily. Here is what which-key shows me after typing C-x 8 "

I use this so often that I would like to use C-x 9 as an "alias" for this binding.

Unfortunatelly I can't figure out how. C-x 8 " is only a partial binding if I see it correctly. describe-key C-x 8 " doesn't show me anything and just waits for further input. It also doesn't seem to be

Ideally I would like something like

(set-global-key-alias-or-so "C-x 9" "C-x 8 \"")

or

(global-set-key (kbd "C-x 9") 'whatever-is-behind-C-x-8-\")

Answer 1

I can think of a couple of ways to do this. The main practical difference is whether you see C-x 8 " or C-x 9 in the minibuffer while waiting to read the next key.

Option 1 is to simulate the user actually typing C-x8":

(global-set-key (kbd "C-x 9") #'my-ctl-x-8-double-quote)

(defun my-ctl-x-8-double-quote ()
  "Simulate typing: C-x 8 \""
  (interactive)
  (dolist (event (nreverse (list ?\C-x ?8 ?\")))
    (push (cons t event) unread-command-events)))

Option 2 is to bind C-x9 to the same keymap used by C-x8" (which is defined in key-translation-map):

(define-key key-translation-map (kbd "C-x 9")
  (lookup-key key-translation-map (kbd "C-x 8 \"")))

Note that option 2 requires you to figure out where that prefix keymap lives (C-hb helps with that), while option 1 can be used even if you don't know that information.

See also: C-hig (elisp)Translation Keymaps