Revert "Do not write state if payload is `''`" for MQTT sensor (#81347)

* Revert "Do not write state if payload is ''"

This reverts commit 869c11884e.

* Add test

homeassistant/components/mqtt/sensor.py

@@ -271,8 +271,8 @@ class MqttSensor(MqttEntity, RestoreSensor):
                     )
                 elif self.device_class == SensorDeviceClass.DATE:
                     payload = payload.date()
-            if payload != "":
-                self._state = payload
+
+            self._state = payload
 
         def _update_last_reset(msg):
             payload = self._last_reset_template(msg.payload)

tests/components/mqtt/test_sensor.py

@@ -313,6 +313,12 @@ async def test_setting_sensor_value_via_mqtt_json_message(
 
     assert state.state == "100"
 
+    # Make sure the state is written when a sensor value is reset to ''
+    async_fire_mqtt_message(hass, "test-topic", '{ "val": "" }')
+    state = hass.states.get("sensor.test")
+
+    assert state.state == ""
+
 
 async def test_setting_sensor_value_via_mqtt_json_message_and_default_current_state(
     hass, mqtt_mock_entry_with_yaml_config