Welcome to VMTN. :-)
I have not used smart card with ESXi before so below are my thoughts on your issue.
1. Have you checked/used steps from below VMware Doc ?
2. Though the Smart Card worked in VMware Workstation Pro, have you confirmed with vendor if the Smart Card supports working in a VM through ESXi 6.7 ?
I did read that article, and that is the option available in Workstation Pro, but I just read the part I was overlooking:
A license is required for the shared smart card feature. See vCenter Server and Host Management.
As this is both not managed by vCenter and only the free licensed Hypervisor not full version, it appears it is a feature that is not available to me.