An HP Elite Lapdock and a Note 9 will get you 90% of the setup you want. I have that setup, it doesn't dock into a slot, it hangs on the side with a USB C cable, but the rest is just as you describe.
USB C hubs with power passthrough, 3 USB A ports, and an HDMI port exist too, so you could run the USB display, HDMI, and a keyboard and mouse all from a single USB C port.
It will depend on their port configuration and display link integration though. The HDMI port might try to claim the USB display bus or whatever, and I'm not sure if you can put multiple USB displays on a single port like that. One will definitely work though.