List of steps to reproduce (step by step, including full links if applicable):

• Log out.
• Go to main page of the French Wikipedia: https://fr.wikipedia.org/wiki/Wikip%C3%A9dia:Accueil_principal
• Click the search box at the top of the page once.

What happens?:
The search box is focused, and you can type in it, but the IME selector (little keyboard icon) does not always appear. It seems to depend how quickly after loading the page you focus the search box.

If you click outside the search box and then click again inside the search box, the ime selector does appear.

What should have happened instead?:
The ime selector must appear the first time you click the search box.

Software version (if not a Wikimedia wiki), browser information, screenshots, other information, etc.:
Tested on Chromium 111 and Firefox 111 on Ubuntu 22.10.