I did a packet capture using MQTTfx and on connect it’s using the MQTT protocol to send a connect command, then the server send back an MQTT connect Ack which finalizes the connection. After that it’s send/receive data using MQTT protocol Publish Message. I did not see any HTTP data at any point. There’s always the pubsubclient library, but I’m not sure that it would work with your AT commands. Does this github issue help?
You could also try this github fork