Same problem here. External display connected via a Startec dock, and I can move the cursor, but no other video displays. Eventually, the monitor just turns off. I removed it from the Dock, and just did a straight USB-C to HDMI and USB-C to DisplayPort cable and it still didn't work.
UPDATE: macOS, despite attempting to connect without the Dock, may still have been trying to use the connection software from my Dock. Turns out, in Catalina, you have to approve the system preference for your Dock. System Preferences > Security and Privacy > Screen Recording. Make sure your display driver (which might be listed there) is checked off to allow screen recording, which may be necessary for your display to work, especially if you have a Dock.