Coming back around to the Technical issues at hand:
The specs for that MacBook Pro 16-in say that the requested resolution, 3840 by 2160 can be output by the computer.
But they are at best ambiguous about whether the resolutions cited are available over HDMI. That computer has no built-in HDMI ports, so you would need to use an adapter. And now the devil is in the details.
Given that HDMI was originally designed for HD TV at 1920 by 1080p, use at higher resolutions requires a stretch, in this case to at least to a more recently issued version such as HDMI 2.0.
The Apple USB-C MultiPort adapter has a new version available, model A12119. so if you get exactly the correct adapter, you may be successful:
Use the HDMI port of this adapter with a display, TV, or projector that connects using an HDMI cable. It's HDCP compliant and supports the specifications below, depending on the model of the adapter.
The model number is printed on the retail box and the side of the adapter, near the ports.
Model A2119 is the newest model of this adapter. It supports HDMI 2.0 at these resolutions and refresh rates when used with macOS Mojave 10.14.6 or later or iOS 12.4 or later. It also supports HDR video in HDR10 and Dolby Vision formats when connected to a compatible playback device and display, TV, or projector.
- Up to 1080p at 60Hz
- 3840 x 2160 at 30Hz
- 3840 x 2160 at 60Hz with these devices:
- 16-inch MacBook Pro introduced in 2019
- 15-inch MacBook Pro introduced in 2017 or later
- Retina iMac introduced in 2017 or later
- iMac Pro
- iPad Pro
Model A1621 supports HDMI 1.4b at these resolutions and refresh rates when used with macOS Sierra 10.12 or later or iOS 12 or later:
- Up to 1080p at 60Hz
- 3840 x 2160 at 30Hz
from:
About the Apple USB-C Digital AV Multiport Adapter - Apple Support