And.. this machine is "never obsolete " * 🤣 *

According to emachines 2001 archived FAQ: "eTower 566i, 566i2, 633id, 633irx, , 600is, 633ids, 667ix, 700irs
Cognac Micro ATX (ATX V1.2 form factor) motherboard, TriGem, Korea Intel Socket-370 (370pin PPGA Socket) for Intel FC-PGA Celeron CPUs Integrating on-chip Graphics controller and Memory Controller Hub (GMCH): Intel FW82810, as well as Intel I/O Controller Hub (ICH) and AC 97' Controller: Intel FW82801 onto the motherboard eliminates the need for more expensive graphic and audio add-in cards. "
So is a Trigem.co.kr motherboard called Cognac and appears to match this by the number: https://theretroweb.com/motherboards/s/trigem-cognac-plus
no bios but if like the plain Cognac only supports to a Celery 1000.....

There's some support info thru this link (including bios / manual) though not sure its newer than what you have or will allow Tualatin use - https://www.elhvb.com/mboards/TriGem/index.html

Yeah I looked at that a bit (probably not as well as you did) and the only good bios file I found was here: http://web.archive.org/web/20101214221920/htt … /oem_bios.shtml
Knowing evasive who runs elhhvb and is working on theretroweb if he thought it was good for the congac+ it would be listed (or maybe he didn't have a way to verify??)
What I find odd is that at Retro the Cognac+ pictures show a 2000731 board (like OP) but in the upper link it points to standard Cognac for a 667ix ...the 733i does list Cognac+.
too bad the bios is soldered (like many Intel boards, damn idiots !!) or would be easy to pull and save current and then flash with a few test roms....
further exam shows the 667ix bios with this header:
IBIOSI$31511.EM.0000.D.0102120916 ..H....r...)Br....+...r...)Br...+.>.f`fPfR...f.f...@.f.fZfX.N.J.....J......+fa.f`....x+.N.........fa..TriGem Computer, Inc........Emachines.
and the 733i bios:
IBIOSI$31511.EM.0000.D.0007052014 .......r...)Mv...o)...r...)Mv..g)..+f`fPfR...f.f...@.f.fZfX.N.z.....z.....')fa.f`.....).N.^.....^.fa..TriGem Computer, Inc........Emachines
so both appear to be for same board based on the first string part. Note the 667i has a dave date of 7/2003 and 733i has a save date of 7/2004 inside the zips.
Too bad the archive links to www.priorityonesupport.com do not go deep enough 🙁 If me would use a DL from retro and sub in the .ROM file as a test....
What do you think ? Did I miss something?

Ok guys thanks for all the links what you have found. It's really amazing that there is still so much info about this computer..
I really appreciate all your efforts!!!
There are a few BIOSes that I thought I would try (weekend when better time). But since the BIOS chip itself is soldered to the motherboard, it is of course difficult if the BIOS update fails and the entire BIOS gets corrupted, etc...???
But I'm still going to take that risk....

I spent a bit of time compiling info on various bios versions for the Cognac+. Unfortunately many of the ones for the Euro board version BIOS are missing, one I would like to find is for the "520 Trigem Cognac+ Intel® Pentium® III 1.0 GHz" just to see what the date stamp is...
The newest found BIOS is dated 08/31/2001 for the "T1090 Trigem Cognac+ Intel® Celeron® 900 MHz" attached below. The second newest is dated 07/19/2001....
Be sure to read this page at the bottom: http://web.archive.org/web/20101214221920/htt … /oem_bios.shtml