And yes HDMI is totally working. This will certainly pass no FCC certification but it will be totally fine for your hobby project π
The project is now uploaded to https://hackaday.io/project/175832-minimal-raspberry-pi-cm-4-carrier
and the PCB files to https://github.com/PTS93/Minimal-RPi-CM-4-Carrier
Please keep in mind this is nothing but a quick and dirty demonstration. Especially the routing is far from good and completely optimized for CNC milling, nothing you wanna copy
If you leave out the status LED circuits this uses no more than 10 components. It of course leaves out some safety measure that you don't always need, the point is to demonstrate just how little is really necessary to get things going. This is true for many SoMs not just the CM4.