[Решено] language switcher button appear in the menu header

Background of the issue:
I installed the WPML plugin and integrated it successfully. I am trying to have the language switcher button appear in the menu header. The issue can be seen on the page: скрытая ссылка

Symptoms:
The language switcher button shows correctly when logged in, but it does not appear in the menu header when logged out.

Questions:
Why is the language switcher button not showing in the menu header when logged out?
How can I ensure the language switcher button appears for all users, regardless of login status?