Change mqtt library

**Describe the problem you have/What new integration you would like**

The current mqtt library used works fine when sending small data entries and texts, however:
- It can not send any data messages which are bigger then the underlaying buffer size of the network adapter (a little bigger than 1KB). No splitting, just dropped. (https://github.com/marvinroger/async-mqtt-client/issues/195)
- It does not properly handle binary messages received. The library calls the call back function multiple times with varying size. No data is lost, but one single 1024kB message can be split up into multiple parts. (Could depend on general load of the system, as it varies for me all the time)
- A lot of other bugs: https://github.com/marvinroger/async-mqtt-client/issues/196

It's thus hardly usable in case you want to stream data in/out of the i2s bus system.

Would be good to migrate to https://github.com/espressif/esp-mqtt and add binary data support to the esphome interface if possible.

**Please describe your use case for this integration and alternatives you've tried:**

**Additional context**

No files, tests, or entry points are named; start by locating the current MQTT integration and reviewing the linked async-mqtt-client reports. Compare those findings with the proposed esp-mqtt migration and binary-data support. Done would require a defined migration scope and verified handling of the described large and binary messages.

Written by the indexing model from the issue text.