Cleanup redundant mqtt entity constructors (#100939)

* Remove redundant mqtt entity constructors

* Remove unrelated change

* Follow up comment

* Revert changes to mqtt update platform

---------

Co-authored-by: J. Nick Koston <nick@koston.org>

homeassistant/components/mqtt/sensor.py

@@ -130,22 +130,12 @@ class MqttSensor(MqttEntity, RestoreSensor):
     _entity_id_format = ENTITY_ID_FORMAT
     _attr_last_reset: datetime | None = None
     _attributes_extra_blocked = MQTT_SENSOR_ATTRIBUTES_BLOCKED
+    _expiration_trigger: CALLBACK_TYPE | None = None
     _expire_after: int | None
     _expired: bool | None
     _template: Callable[[ReceivePayloadType, PayloadSentinel], ReceivePayloadType]
     _last_reset_template: Callable[[ReceivePayloadType], ReceivePayloadType]
 
-    def __init__(
-        self,
-        hass: HomeAssistant,
-        config: ConfigType,
-        config_entry: ConfigEntry,
-        discovery_data: DiscoveryInfoType | None,
-    ) -> None:
-        """Initialize the sensor."""
-        self._expiration_trigger: CALLBACK_TYPE | None = None
-        MqttEntity.__init__(self, hass, config, config_entry, discovery_data)
-
     async def mqtt_async_added_to_hass(self) -> None:
         """Restore state for entities with expire_after set."""
         last_state: State | None