[Решено] language switcher not working in translated pages

Background of the issue:
I am trying to add a custom widget of the language switcher in the navigation using [wpml_language_selector_widget]. I am following the documentation at https://wpml.org/documentation/getting-started-guide/language-setup/language-switcher-options/adding-language-switchers-using-php-and-shortcodes/?utm_source=plugin&utm_medium=gui&utm_campaign=languages.

Symptoms:
The language switcher is only showing in English. When I select another language, the language switcher dropdown is not showing.

Questions:
Why is the language switcher not appearing in other languages?
How can I ensure the language switcher works for all languages?