I also have a similar issue. My use case is slightly different, I have two CalDigit TS3+'s going to 4x4k displays. I plug 2 monitors into each CalDigit and 1 cable into each side of my MBP. The MBP is in clamshell mode. I was using this setup with my last generation MBP and it was ok. When I got the 16", I also upgraded to Catalina on both the old and the new. I experienced these issues then with both laptops, so I believe its related to the Catalina and not the hardware.
In my case, when I plug in the first Cal-digit, I hear a beep and my USB accessories come to life. When I plug in the second I hear nothing. I'm not sure if that's because its already failed or the second one has an impact. As with others, the laptop was sleeping when I connected it. In my case, the screens flash for a while (like they are trying to initialize) and eventually it reboots with mixed results.
In one instance, the computer booted into password recovery. I choose the startup disk but instead of rebooting, I just plugged in the Cal-Digits again. The computer hard locked, right in the recovery OS.
I am running the latest firmware for the TS3+ and I just updated to 10.15.2.