Add support "publish state" for fan component

Hello, like the switch component, I hope we can add the support of "publish state" function for the fan component. I add a template output to a speed fan, then if I receive a rf433 code, the state of the fan should be changed.
**Describe the problem you have/What new integration you would like**

I add a template output to a speed fan, then if I receive a rf433 code, the state of the fan should be changed. But now we only support "turn on" and "turn off". If I want to change the state, I need to use "turn on" or "turn off". and the fan component will do an action too, not just change the state of the speed fan. Thank you.
**Please describe your use case for this integration and alternatives you've tried:**

**Additional context**

Start by comparing the fan component's current state handling and publish-state behavior with the switch component, then trace how template outputs and RF433-triggered updates reach the fan. Done means the fan state can be changed without triggering a physical fan action while existing turn-on and turn-off behavior remains intact.

Written by the indexing model from the issue text.