yea the app definitely has no bubble feature, that requires us to post a notification with a conversation ID and to use a Person. Neither of which is done 
The permission is used for notification commands command_activity and command_broadcast_intent because in those cases the app is telling another app to open up and do some action.
Some examples in the docs: Notification Commands | Home Assistant Companion Docs
You can do things like launch GPS navigation to a certain destination. Depends on the app, its an advanced feature but lets you do some cool stuff! This post tries to capture as many known intents and actions as we can find: Android Intents - Sending & Receiving List (Starting Activities too!)