Installed the manufacturer's smart card reader driver into the VM and updated the device to use the manufacturer's driver instead of the generic Microsoft driver. VM detects the reader in both shared and passthrough modes, but the smart card is no longer detected by the guest.
I decided to load the VM image into VMware Workstation Player 15 out of curiosity and the smart card was detected.
I am still unable to determine why the smart card isn't able to be accessed by VMware Workstation Pro 15. Next step is to reinstall Workstation Pro 15.