Improve climate turn_on service (#94645)

homeassistant/components/climate/__init__.py

@@ -534,6 +534,14 @@ class ClimateEntity(Entity):
             await self.hass.async_add_executor_job(self.turn_on)
             return
 
+        # If there are only two HVAC modes, and one of those modes is OFF,
+        # then we can just turn on the other mode.
+        if len(self.hvac_modes) == 2 and HVACMode.OFF in self.hvac_modes:
+            for mode in self.hvac_modes:
+                if mode != HVACMode.OFF:
+                    await self.async_set_hvac_mode(mode)
+                    return
+
         # Fake turn on
         for mode in (HVACMode.HEAT_COOL, HVACMode.HEAT, HVACMode.COOL):
             if mode not in self.hvac_modes: