Grmph, I was unable to roll back because whenever I now uninstall avast, it wipes out my settings, and when I install the old version, it immediately automatically updates to the latest 2021 version.

So I gave up, did system rollback to 2021 version with my latest registration/settings, and checked what IP addresses avast needs open to phone home to get the service working. It turns out that even with the proxy setting enabled, it tries to connect to IPs in these ranges directly:

195.39.12.0/24 (r-X-12-30-195.avast.com)
159.253.143.0/24 (aXYZvg.avast.com)
77.234.40.0/21 (r-X-Y-234-77.ff.avast.com)

When it can’t connect to (some of?) these, the service stops working. (BTW, accessing the support/feedback page from avast UI requires direct access yet another range to work at all, but that doesn’t bother me that much.)

So I added exception rules to allow direct connection to these machines to make it work for now. Once added, the service is finally able to start.

But I hope someone from the avast dev team will finally realize there is a problem on their side and get this fixed. Program which doesn’t work properly or even crashes just because it can’t phone home feels pretty lame, doesn’t it? And if you can’t get even the elementary networking right, how is your product to be trusted?