[Закрытые] Language switcher to Menu

Background of the issue:
I am trying to add a language switcher to the menu on my WordPress site using WPML. Here is a video of my attempt: скрытая ссылка. The issue can be seen on this page: скрытая ссылка.

Symptoms:
I cannot save the language switcher to the menu despite trying 5 times. I can only close the settings screen using two different 'X' icons. I have cleared the cache for WPML in the troubleshooting section, but the issue persists. I expected to see a menu with 2 flags on the right for EN and NL, but instead, I just see the menu without flags and switcher.

Questions:
Why can't I save the language switcher to the menu?
How can I resolve the issue of the missing flags and switcher in the menu?