Finally, all the mystery with this VIA-instead-of-intel-chipset solved.
On some now "forbidden" part of the internet I found link to this video. The mobo from this YT-video looks exactly the same compared to mine minus the sticker with label "BX-6AV2" (over the painted on the PCB "BX-6AP2" label). This led me to try some BIOSes for the FordLian/Polaris/RedFox BX-6AV2 motherboard version. I downloaded all the available BIOS dumps from theretroweb website for the model BX-6AV2, flashed the newest BIOS version 2.5 from FordLian mobo, but the motherboard still doesn't boot (instant hang at "C0,--" code). Next I tried the version 2.4 (also from FordLian mobo, but bin-file is mistakenly named as for RedFox) and yes, this time the board boots normally with its native BIOS. I tested the floppy drive - surprise, now it works too! Out of curiosity I tried the oldest available BIOS ver. 2.2 (this one is from RedFox board with very nice foxy boot mini-logo instead of standard "pollution" picture) and it work just fine too.
I don't know what's wrong with the newest BIOS-dump version 2.5 from FordLian/Polaris board, maybe the zipped bin-file is broken or maybe it's somoene's another BIOS-modding-mess, but for now I'll use version 2.4 which works fine.
So, it turned out that all the troubles with my BX-6AV2 board (including wrong mobo BIOS flashing many years ago) were due to someone in the factory has forgotten to stick a sticker (no pun intended) with the correct model (BX-6AV2) for this VIA-chipset version over the painted incorrect BX-6AP2 caption.
Mystery solved. One very nice Slot 1 motherboard revived. And I learned a lot for Award 4.5xx BIOS modding, last - how to change chipset init-table * 😀
Now I'm looking for healthy BIOS-dump version 2.5 (or newer if available) for FordLian/Polaris/RedFox BX-6AV2 mobo...
P.S. NSSI an HWINFO recognize the northbridge correctly as VIA VT68C692BX chip. The info on theretroweb's BX-6AV2 page is totally wrong and misleading: the chipset is not VIA VT82C693 (Apollo Pro+), but VIA VT82C692BX (Apollo Pro II / BX) and all of this motherboard variants (BX-6AV2, BX-6AP2 and ZX-6AP2) lack any integrated sound chips! And of course the newest BIOS version 2.5 from FordLian BX-6AV2 mobo is sc**wed up.
* - 'couse I'll forget this after some time: find the string "CHIPSET FEATURES SETUP" in uncompressed ORIGINAL.TMP, right after it there are some repetitive "02 xx xx xx xx xx 00" hex-patterns - the "xx" bytes sets the chipset registers
from СМ630 to Ryzen gen. 3
engineer's five pennies: this world goes south since everything's run by financiers and economists
this isn't voice chat, yet some people, overusing online communications, "talk" and "hear voices"