To have your menu appear in one of your target languages, you need to first add translated Pages or Posts to the menu that is currently being used. Menu items in a particular language will only display when viewing the site in the respective language.
Under Appearance > Menu, you will see the list of menus you are using. The menus surfacing on your website are displayed in the primary navigation field.
You do not need to create separate menus for each language. Instead, add the translated pages to the menu that is already in use. The translated menu items will only appear when viewing the respective language.
When using custom links, you can adjust the straker_lang option to one of the target languages
The language flags indicate the pages that have been translated will be displayed on the menu. The admin menu UI will only display the translated pages in the menu structure at the bottom of the menu. Drag and drop as required.
You can send menu content for translations as a .po file. When you are re-importing the .po file (.po compiles to .mo files) make sure you adjust the language codes so that the translation can be surfaced.
You may need to customize any additional plugins for displaying menus if they override the Straker Translations settings. Please refer to the help documentation for the menu plugins you are using.