Use eager_start for homekit task creation (#111675)

homeassistant/components/homekit/__init__.py

@@ -256,7 +256,8 @@ async def async_setup(hass: HomeAssistant, config: ConfigType) -> bool:
                 DOMAIN,
                 context={"source": SOURCE_IMPORT},
                 data=conf,
-            )
+            ),
+            eager_start=True,
         )
 
     return True

homeassistant/components/homekit/accessories.py

@@ -610,7 +610,8 @@ class HomeAccessory(Accessory):  # type: ignore[misc]
         self.hass.async_create_task(
             self.hass.services.async_call(
                 domain, service, service_data, context=context
-            )
+            ),
+            eager_start=True,
         )
 
     @ha_callback