Climate Zones

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

I would like to be able to associate multiple climate thermostats together, so that `run_time` and `off_time` timers are shared between the thermostats, and `deadband` settings are ignored when heating or cooling is active on any one of the thermostats.

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

When using a multi-zone heating system, it makes sense to have a climate thermostat for each zones. But some settings should apply to the entire heating system, not to the zones. Like `min_heating_run_time` and `min_heating_off_time`, these are to protect the heating system and prevent short cycling. But once the heating system is on, because one zone is on, the as long as all zones don't turn off before min_heating_run_time, individual zones do not need to stay on for that duration. Additionally, once a zone is on, `heat_deadband` can be ignored. Once the system is running, it would be beneficial to ignore the deadband and start heating every zone up to `heat_overrun`, again to minimize the startup cycles of the heating system and avoid the case of one zone reaching temperature, and shutting off the heater right before another zone passes the deadband and starts calling for heat.

**Additional context**

The request does not name files, tests, or an entry point. Start by locating the climate thermostat integration and reviewing how multiple thermostats currently handle run-time, off-time, and deadband settings. Done means the shared multi-zone behavior is defined, implemented, and covered by tests for coordinated heating and cooling.

Written by the indexing model from the issue text.