The issue seems to be that the Digilent Adept 2 Runtime was not installed. See also: Supported EDA Tools and Hardware and go to the link above for instructions. My mistake was not understanding that the ZCU-102 board has this module on it.
Also, I had installed the Xilinx JTAG drivers (/opt/Xilinx/Vivado/2020.2/data/xicom/cable_drivers/lin64/install_script/install_drivers/install_drivers) on advice from co-workers. This was probably right for using the Xilinx JTAG tools, but not right for HDL Verifier.