Try your Y splitter with the mouse and keyboard switched... some be like that, I know not why.

not all PS2-combo ports and Y splitters are equal.

Some just route the signals to the same pins on all connectors.
The msi board I have, it's either mouse or keyboard. both just didn't work out for me. and since the signals can differ, I doubt it will work out for anyone, even with a straight Y splitter

Some used the nc signals in the mainboard ps2 port for the other signals, ie, normal portlayout for keyboard and unused signals for mouse.
My compaq armada has this setup, one ps2 port on the laptop, with a Y-splitter that routes the normally unused nc pins to one of the ps2 connectors, thus allowing both mouse and keyboard to be used. must use appropriate ps2 connector for mouse & keyboard.

Since you mention you have only one ps2 port. What mainboard is it ?

I did the switch - it's one device or another ... - now KB works and no mouse.

So far ...I tried only one Y splitter which doesn't work on my motherboard (Biostar X470 GTA), nor a Asus H81 CSM ( this one has two PS2 ports ) Also a Gigabyte Z68 motherboard didn't like either this Y adapter. (this Z68 motherboard has only one PS2 port which is bi-color magenta/green, my kb is solid magenta, but I guess it doesn't mean anything)

There is also a kdbclass.sys file which is in charge with keyboards. (replaced it with the NT 4.0 version - still no change...)

I did update driver from AT keyboard to Microsoft KB ... and now it's gone, only USB keyboard shows up...

if you've got a multimeter you could measure out the Y splitter and see if it's straight or not.
if it is straight, as in, pin x = pin x on all connectors. I'd say chances of keyboard & mouse working together are close to zero.
if not, then it would depend on your mainboard,
and well the mainboard I've got, it's actually a Gigabyte GA-H55M-UD2H not an msi, also has a dual color ps2 port,
yet it only does PS2 KB or mouse. not both at the same time. I would've expected it to work with a splitter but... no it does not.

Well, I guess even if the cable is good still won't work without some BIOS support. Asrock motherboards, even the latest X570 ones, have a PS2 Y-cable option in BIOS.

Because this AMI BIOSes are a collection of tiny modules and there are tools to play around... I was tempted to extract such a module from an Asrock X470 motheboard (PS2 module has 20kb) and use it on my motherboard, then I found that Asrock uses a different Super IO Chip. Mine is from ITE and Asrock uses NCT6791D from Nuvoton. Operation aborted.