Thank you P1LGRIM for reconfirming!
I re-added the kext again:
and the structure of the kext looks like this:
I'm waiting for Fenvi to send me a replacement card, should arrive in 2 days.
I'm really puzzled about this. I don't believe in magic, somewhere in my process there was a glitch that locked me out of any access to the internet.
At this point, I've tried all combinations of GPU PCI and my Fenvi. In position 2 and 3, Fenvi doesn't even show up in my system report PCI, that's the only difference.
I am also on my second motherboard, identical, yes, but if there was any issue with my first one, that would hopefully be solved by its replacement.
I just reinstalled my Big Sur from scratch using my original boot USB - smooth installation to a spare SSD. Works great - just no internet.
I have very little hope for Fenvi replacement - the one I have works well on Linux Mint liveUSB, at least I think it worked great with this network card and not my original built-in intel.
I already mentally prepared myself to the fact I might not have wifi at all on my new machine, and will have to live with cable ethernet only, but even that gives me trouble. (this may still be an outside and non-related issue, I don't plug my cable directly from the router to my motherboard, but rather use wi-fi extender that has ethernet port. But I need to make sure that extender is solid, I'll do this test using my MacBook pro when rj45->USBc adapter arrives later today)
I think at this point is the only thing I haven't tried was to recreate my EFI from scratch and run another install of BigSur.