I wanted to add a couple of new symptoms. If the MBP is closed and the monitor is connected it will power on and give me the log in screen for the encrypted HD on the external display. However, once it starts to load the OS the external screen will go black and not come on again. If I lift the lid on the MBP it will be at the desktop and act like the external monitor is on (extended desktop).
Also, when the CPU usage spikes the external monitor will go black, come back on, go black and then come back on.
All of this behavior is post 10.15.4 install.
For what it is worth the System Profiler shows both displays connected to the Radeon Pro 5300M on my 2019 16" MBP.
It also shows the chip set in the HP USB-C G5 Dock as Microchip Tech. But that could just be on the USB 3.1 and PD side of things.
And lastly, once I do get it working through various fidgeting (mostly plugin, unplug, plugin, unplug, plugin...until it works) if I put the laptop to Sleep rather than Shut Down it will reliably start the external monitor on wake. I have done this over a couple of days now. So, there is just some disconnect when the OS (drivers?) loads at start up. And the weird screen flicker at high loads.
I have also come to realize that the dock is no longer charging the battery. The System Profiler shows that the power supply is connected and delivering 75 Watts. But it will not show as charging. The 96W adapter from Apple works fine plugged in to another port. So, may be a USB-C PD negotiation problem post update.
Just wanted to add a few more details incase anyone at Apple is following. :-)