All I can confirm is that you can update the FW in 2940UW. No idea about going from non-R to R with just different FW.
My card was originally 2940UW/GE and my guess GE stands for German Edition since it did use that language. I wanted to update the FW to get past some limitations of the early FW (like 8GiB limit) so now my card has standard English FW.

The files I found were called afuv220.exe (for v2.20.0) and afuv1343.exe (for 1.34.3) - these are different family, the 2.x supports SMART and some other advanced stuff but if one doesn't need it then the late 1.x has all the typical issues fixes as well. There's also 2940u2w_bios_3100.zip but that's for U2W model (which I have as well but I didn't update it yet). Sadly I can't remember where I got these files but perhaps searching for these filenames will help.

Deunan wrote on 2023-06-29, 11:37:

but perhaps searching for these filenames will help.

Thanks, can try filenames. Anyway, I did some extensive testing and found out that Adaptec 39320 (non R) is actually utter and ultimate CRAP.
Well, first tried under ubuntu (fresh install) - somehow disks appeared as raw devices under linux. Switched linux and to my horror
RAID0 and RAID1 appeared as mdraid. As multipath devices. No adapter based mirroring or striping - host based.
IDK what ever lies Windows drivers will tell, but under linux they appear as multipath / duplicate.
So far, so bad. I specifically took old uw2 4GiG harddrives for testing. Just so see speed differences more clearly
Results:
HW stripe no redundancy - 40 MiBs
LVM stripe 4 devices - 50 MiBs
RAW HDD single disk performance ~20-- MiBs
Chimera RAID HW RAID1, LVM stripe "stripe of mirrors"
WORST ever... 10MiBs
Chimera RAID HW RAID0 LVM mirror "mirror of stripes"
20 MiBs. Half redundancy gained exactly losing half of performance. This was expected.
Tested with 4GiG file ... so all buffers and caches get filled and I can see RAW write performance. WITH buffers still available 200MiBs was the best. Only with LVM chimera raid and RAID0 LVM. Also LVM RAID showed ~200MiBs way longer. Almost up to first 900MiB or so copied. Logical - it uses system memory.
Testbench was pretty old Pentium D, Asus P5PL mobo. 200MiBs raw is the best it can do ... even with respectable controller and SSD disk.

Here are the official downloads for Adaptec products (including firmware), you probably already looked here but just in case not: https://storage.microsemi.com/en-us/support/scsi/