Impossible to Sync the Template entity with the original one

[NdR91]

If this integration is used with an already existing Climate Entity, it won't be possible to sync them properly.

For example if I turn on my Daikin AC from the Original Integration, the Templated Entity won't turn on.
Same for tthe target temperature, the fan mode, the swing mode and the hvac mode.

I tried to set those mode template with the attributes of the original Climate:

fan_mode_template: "{{ states.climate.original_entity.attributes.temperature }}"

But doing like the above example, will cause issue when I try to change the temperature itself because it will be fixed to the original entity.

[elliotwestlake]

I put a response in #37 which should hopefully help!