USB-C port not working as a host to use with USB OTG or HDMI adapter
It turns out that my device is not HDMI-compatible and will not transmit over that adapter (or any other, apparently).
Props to Robert for finding a (generic?) listing over here:
https://en.everybodywiki.com/List_of_devices_with_video_output_over_USB-C
(In case anybody else is googling this and can't find a solution, I highly recommend checking your device against the list above.)
Whereas at first I was a little skeptic of this insight, buying a USB-C to USB-A adapter and testing out with other devices like a USB mouse or keyboard confirmed that the port itself has no issue - it's the HDMI output that has a problem.
I'll look into alternatives on how to cast my screen in another way.