Currently the app can be controlled via the Intents API but it’s a little clunky and it relies on android’s intent system, which they could decide to change at any moment. MQTT can easily be configured for 2 way communication. Please could you add in the ability to send messages to the app as well as from.
In Home assistant you’ve added a blueprint to send intents but again, its a little clunky, and requires a new script for each action. With this you could add in buttons to the integration to send straight over MQTT, without the need to interact with Androids Intent system. (It would also allow anyone using MQTT for other projects to send messages too)