must be more clear and be in the app contructor

I disagree. If you use communication like MQTT you should not do everything in a constructor of a class. Assynchronous approach is the right one, especially when using assynchronous frameworks like Qt.

You can also do that with assynchronous APIs. But from your description it is not clear what should NOT happen until you get the result from MQTT.

At the start of my app I create the main app structure in memory reading from a base file. After that this structure must be tuned according the information from the MQTT topic. In the end of the contructor I set ready_fl=true;
In other words I must be sure that MQTT topic had been read before the structure tuning starts.

Theoretically, I can create my main structure inside MQTT callback and set ready_fl also in the callback, but I somehow don't like it - the initialization sequence must be more clear and be in the app contructor.

But I need to read an MQTT topic right on the app start

You can also do that with assynchronous APIs. But from your description it is not clear what should NOT happen until you get the result from MQTT.