Rework mqtt climate platform to simplify implementation water_heater platform

[jbouwh]

Proposed change

PR #93644 implements the water_heater platform. This platform has a lot in common with the climate platform.

This PR isolates the code that can be shared to set up both entity types.
The new MqttTemperatureControlEntity class implements MqttEntity and implements the shared code to subscribe to topics, handle incoming messages, and control target temperature.
The MqttClimate base class inherrits MqttTemperatureControlEntity.

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[home-assistant]

Hey there @emontnemery, mind taking a look at this pull request as it has been labeled with an integration (mqtt) you are listed as a code owner for? Thanks!

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[jbouwh]

@hookedonunix I also have splitted the climate specific parts from the common parts. Initially I added them together, but I guess it starts getting messy if the water_heater parts should be added here to. Now this can stay in your PR. You could leave out the shared parts and keep the specific parts in water_heater.py.

[emontnemery]

LGTM, thanks @jbouwh 👍

[hookedonunix]

Looks great, thank you!