I had been experiencing the same problem since updating to Monterey - and I do use Cisco AnyConnect. After reading all 11 pages on this thread until midnight last night, I did one last hail-mary google search - and I found a fix that has kept my connection ON ALL DAY today.
I followed the advice in the third solution on this page - which isn't exactly about the dropped internet connections, but does make references to many of the topics brought up in this thread.
https://apple.stackexchange.com/questions/420773/the-process-com-cisco-anyconnect-macos-acsockext-hogs-mac-cpu-but-cannot-be-kill
In a nutshell, the solution that worked for me:
Go into the Applications folder and open the Cisco folder.
Delete the Cisco Socket Filter application but NOT the Anyconnect client.
I have a 2019 iMac running Monterey 12.4. This problem didn't seem to start immediately after the update - maybe a week later? All of a sudden I was dropping internet connection (every few minutes). I assumed it was the access point or the modem, so I wasted a bunch of time resetting those. Then I realized every single other device was working normally. Only my computer was dropping the connection. I did all the wifi setting changes others have tried, with no luck. Rebooting in safe mode, then in normal mode, seemed to help, but only for about an hour - then back to dropping the internet connection every few minutes. Had to use my phone as a hotspot to get work done. I did notice that on Chrome I would get the DNS Error screen, followed by the No Internet screen - as described throughout this thread. If I let it sit and spin for 30-90 seconds, the connection would come back (and then drop again after a few minutes). Rinse and repeat.
I should also mention that over the past several days I've heard the fan come on inside my computer. The back was very hot to the touch. This was mentioned in the page I linked to above. Since deleting the Cisco Socket Filter application, my computer isn't getting hot any more (at least not all day today). I tested the connection to my work VM - successful. Pages have been loading in all browsers, all day.
Right now I'm praying I didn't just jinx myself by declaring this problem solved on this machine.