Can't change keyboard input language on Ventura

I have English and French setup as my keyboard input languages (see image below).

I have enabled the Language switching menu (see image below).

Yet, the menu does not appear at the top right of my screen (see image below).

I have also enabled the ^-spacebar shortcut for switching languages (see image below), but pressing that key combination doesn't change the input language.

As a result, I have no quick way of switching language. I have to go into System Settings > Keyboard > Language every time, and it's annoying because I often change from one language to the other.

Anuy help would be appreciated, thgx.