TL;dr: re-install Kaspersky, but also delete network card drivers!
I fixed this problem! First in-game web stuff wouldn't work, then I realized even Steam wouldn't work. I could download games, but not browse the store or workshop, etc. Even Spotify wasn't loading the homepage or searches, just saved playlists. Chrome/Edge still worked this whole time. The final straw was Windows couldn't see the internet even. Windows updates, syncing onedrive, etc., didn't work. When i disabled Kaspersky it would all work, but as you said, turning off individual features didn't fix it.
Someone, somewhere, said to re-install Kaspersky, and someone else said to delete all network cards. I backed up my Kaspersky settings, uninstalled it, restarted, went to device manager, deleted all the network cards (didn't bother removing the drivers from the system, just deleting the devices from device manager). Then re-installed Kaspersky. I think it even remembered my settings. This fixed it!
My theory is that Kaspersky used a fake network card for it's firewalls and protections. Then they updated something in the program and that fake card became orphaned and conflicted with the new one. Chrome and Edge probably find their own path to the web and they could deal with it, but Windows kept thinking the fake network card was
the path to the web, when it was a dead end. Chrome did take a minute or two to establish connection, but I got to play the dinosaur game...