As it turned out, replacing the problematic machine brought on success. With the following configuration it is possible to execute fastboot without it blocking:
HP EliteBook 820 (G2)
Debian Bullseye, Linux 5.10.0-8-amd64
As sole kernel on bare metal, without hypervisor or competing virtualization.
So it seems to not be an issue with Linux as such, but something more intricate which I do not intent to spend any further time on investigating. My strongest suspect is that the problem might be related to having several virtual machines sharing the same hardware and being configured to have concurrent USB access.
Thanks @gnection and @tcecyk for your replies! For what it’s worth, trying to retrieve the CID resulted in fastboot getting stuck on the original host in exactly same way as when attempting to retrieve oem unlock codes.