Is this the same as this known issue from VMware? If so, this is not an AnyConnect-specific bug.
VMware Fusion 12.1.2 Release Notes
Known Issues
- The virtual machine (VM) cannot access the same network as the host while macOS Big Sur host is connected to the virtual private network (VPN)
If the Big Sur host is connected to VPN, then the VM cannot access the same network as that of the host. - Workaround: Connect to the VPN in the VM instead of connecting to the VPN on the host.