Here are some comments that may be helpful to users experiencing issues with the Anyconnect 2FA on Linux.
In the past, there was an issue where the 2FA window did not display its contents on some Linux distributions (I tried Ubuntu, Fedora, Mint, and Arch) because the lib32-webkit-gtk package was missing. Installing the package fixed the problem.
Recently, I noticed the same problem returning in a slightly different way. The window was now still not displayed, but the elements (button, text field for login) were accessible through the UI, even though they were not rendered. After some tinkering, I found out that the problem is that AnyConnect appears to not work under newer Nvidia drivers. A downgrade to older drivers, or the open-source nouveau drivers solves the issue.
For obvious reasons, downgrading graphics drivers is not desirable. You can solve the issue by installing the openconnect-sso package and accessing your vpn through the terminal. There the SSO web-popup appears to work regardless of what version of graphics drivers are installed.
I hope this helps.
