I personally create new translation file module.php and put there all stuff not related to any of direct entity.
Things like that(sidebar category, section etc.) would go there (tasks::module.sidebar.title)
But you can do as you like You got all the freedom of laravel and asgard tries not to require specific files and names.
@TheLionKing you shouldn't really have two separate apps that use code (i.e. Models) from one of the two apps, this is why @nWidart is suggesting you use an API, so that one of your app is the central source of all of your data, and the other app simply consumes it.