Thanks for posting this! I also found that once the Cisco client is connected to the VPN in the Hyper-V VM, then I could turn the "Enhanced Session" mode back on to use my additional monitors while the VPN is still connected. (By the way, if it is helpful for anyone, the "Enhanced Session" mode setting is in the "View" menu of the Hyper-V Virtual Machine Connection window.)
Only for searching and indexing purposes, I want to specify that the exact Cisco AnyConnect error in a Windows 10 Hyper-V virtual machine is the following: "VPN establishment capability from a remote desktop is disabled. A VPN connection will not be established."