I would also like to add that on the menu I use the opposite language switcher and it only displays the non default language “EN”.
So when the visitor has selected the English language there is no way to switch to the local language, using the Menu Language Switcher.
When I choose to use both of the language flags on the menu, both of them link to the “/en” version of the site.
Please keep in mind that the “Floating Language Selection” works as expected.