Ciaran, SOLVED!
I followed your suggestions by switching to a different Template Style for each language. Awesome, the Login and Language Switcher show up now in the Main Menu as dropdown menu and both are working fine and smooth!! Thanks!!
For those who might run into the same issue by trying to install a Multilanguage website with Emani, here are the steps, in a nutshell (fresh Joomla 4 setup, installing the Template Emani without demo data sample):
1) Add the languages: System > Install > Languages.
2) Enable Content Languages: System > Manage > Content Languages > enable your languages.
3) Enable the 2 language plugins: System > Manage > Plugins > enable “System Language Filter” and “System Language Code”.
4) Create categories for each language. I named them "Category EN", "Category DE", etc. Remember to choose the correct language (right sidebar). Try using the same alias for each language, adding "-en", "-de", etc. This way you work more organized.
5) Create articles for each language. Select the correct language category. Choose the correct language.
6) Create one Main Menu for each language (leave the Main Menu that comes by default untouched, do NOT rename it). I named my new main menus "Main Menu EN", "Main Menu DE", etc.
7) Create items for each Main Menu EN/DE/etc.
8) Select any menu item for each language and set the "Default Page". This will be your "Home" page for each language. Enable it in the column "Home". A language flag appears.
9) Create a new Template Style for each language (duplicate) with Emani by following this tutorial:
https://joomla51.com/tutorials/joomla-basics/creating-multiple-template-styles.
10) Select the Main Menu to be used in the language Template Styles: System > Site Template Styles > Emani - Default EN/DE/etc. > General > Menus > Select Top Menu: choose the corresponding Main Menu for your language Template Style.
11) Enable the Language Switcher as a dropdown menu in the Main Menu EN/DE/etc. by following this tutorial:
https://joomla51.com/tutorials/template-extras/adding-a-module-to-the-menu-dropdown.
12) Remember to use the Association function that comes with Joomla 4: Components > Multilingual Associations. This is important. Do not skip this. Done!
Nice option we have with "menumod-". Love it. Love Emani.
Cheers!