Alright, I struggled to make it work for a total of 5 hours. The original issue was that Firewall could not start because of error 1068 - some dependency failed to start. The symptoms: outgoing connections work, incoming are blocked. I drilled down to Windows Firewall Authorization Driver malfunction.
Tried just about every advice out there on the internet - nothing worked. Having gathered enough frustration, I thought it would not hurt to uninstall this crappy thing from Device Manager.
No problem, right click -> Uninstall, reboot, and guess what - the firewall is up and running, with all configuration preserved just as I left it. The only exception is RDP, which died due to some other dependency issue. Luckily, it’s the only non-working function, which is not so critical.
If you have the same issue, here’s the way to fix it:
Device Manager -> Menu -> View -> Show hidden devices -> scroll to Non-Plug and Play Drivers -> Windows Firewal Authorization Driver -> right click, choose Uninstall and confirm all further prompts, reboot when done.