I used this link and it worked for me! It was a battle all day but so far it hasn't logged me out.
I was even able to 'Allow' the extension in Privacy & Security in Settings which I was not able to see with other Cisco AnyConnect VPN Client software.
Link to Big Sur AnyConnect VPN Client - https://developer.apple.com/forums/content/attachment/d3a06295-e5c0-4648-8d06-d8014c7269b2
clc808
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I have this same issue. I am trying to install Cisco AnyConnect VPN Client and the final step to 'Allow' the extension in the Security & Privacy window does not show.