Correct, you need a script.
It will be easiest to help if you show us what you tried and where it went wrong.
I recommend using Blockly if you are not already familiar with programming languages. But to send MQTT in a Blockly Script you’ll need to install a Block Library: MQTT Actions
You can find that in MainUI → Add-on Store → Automation → Block Libraries. Add MQTT from there and you’ll find the MQTT blocks under “Libraries”. It provides a “publish MQTT message” block you can use to publish the state of the Zwave Item.
Note that you only need the MQTT Broker Thing to use this. You don’t need a separate MQTT Generic Thing to publish a message like this using the MQTT action.
If you don’t want to do it that way, link an Item to the “test_sensor3_mqtt_channel” Channel and in your Script, sendCommand to that Item the state of the Zwave Item. You don’t need the Block library for MQTT to do that.