Thinking I might have a hardware issue with the Mac itself, I opened a case with Apple, and found the following:
The adapter does work on this computer, but only on one specific port - the front port on the left hand side. It is not recognized at all on the other three USB-C ports. At an Apple store, the behavior was the same on another Mac of the same model, 15-Inch MacBook Pro (2018).
Apple didn't have an explaination or a fix, but knowing that it works in this specific port, I'm able to use the cable.