Yes, I checked the antenna and it’s connected to the LoRaWAN card.
The starter kit is bought in this year. The firmware of Conduit is 1.4.3.
Right, everything points to the node not transmitting at a frequency the gateway is listening on or it using private sync as suggested by @jreiss.
The best way to check this assumption would be to use a node that is known to work with TTN and check if you see traffic from it. However that might be hard to get. Next best thing is to get a node with a different LoRa module and use that to test. The TTN node comes to mind as it has plenty of sample code available.