I know this thread is almost 4-years old, but I am having the same problem with my NUC8i5BEK. The USB-C port passes audio but no video at all. I am using a "uni USB C to HDMI Adapter 4K | High Speed HDMI to USB-C Adapter | Type C (Thunderbolt 3/4) HDMI Converter" that I bought from Amazon for $7.98
This adapter works perfectly with my wife's Macbook Air M1 Laptop. I don't know if it's a Linux driver issue or the adapter is not compatible with the NUC.