Queue MQTT logs until connected

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

Queue logged MQTT messages if not connected to the MQTT server, and send them once connected.

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

Having a complete log, including messages logged before connecting to wifi/mqtt server is extremely helpful in many cases for debugging purposes. UART logging, even though provides a complete log since the first moments after boot, is not always convenient; for example, in cases when the device is not easily accessible.

**Additional context**

The request names no implementation files, tests, or entry points. Start by locating the MQTT logging and connection-handling entry points in the ESPHome codebase; done means messages logged before the MQTT connection are retained and sent after connection.

Written by the indexing model from the issue text.