I guess this is more a problem of your keyboard. Just google N-key rollover.

I use the keyboard since 1996 and I can tell you that it supports multiple keypresses fine when attached to a native PS/2 port.

I just don't want to buy adapters on speculation. If someone has one that verified supports multiple keypresses I can try to get that specifc model.

Have a look at this one: https://geekhack.org/index.php?topic=14618.0

The adapter has a USB controller inside to present a USB keyboard to the OS. It appears that this controller does not support a high enough value of "N" for N-key rollover. I don't know if cheap brands are more likely to suffer more from this flaw compared to more expensive ones.

Note that USB in general has a limit for this "N", which is the amount of keys you can press simultaneously. There's no such limit on PS/2 (you can in theory press 104 keys at the same time and all of them will register fine, if the keyboard hardware supports that). With USB, you are limited to only 4 keys at the same time AFAIK. But it also depends on which 4 keys (shift + ctrl + D for example might work, but W + D might not.) Some USB controllers are smarter and present multiple input devices to the OS, extending the amount of keys.

I ordered a cheap PS/2-USB converter (for now) that should work.
Meanwhile I tested the key roll over with AquaKeyTest and the ATEN UC10KM adapter shows an interesting behavior:

I can press 2 keys at the same time, when I press a third one it is not registered AND all pressed keys are released.
Also whenever I release a key all other pressed keys are released. This is independent of the fact that they are actually still pressed.
This release behavior just kills the adapter for any use beyond simplest typing.

While at it I also checked a Dell SK-8135 USB keyboard that shows a 2KRO and DAS KEYBOARD 4 Ultimate which shows a 6KRO.

I'll report as soon as the other adapter arrives. If that also shows issues then I guess it's time for a more professional solution.

So I bought this cheap adapter: https://www.amazon.de/gp/product/B003CI7PG4

AquaKeyTest shows that it has a 2KRO but without the strange 'release all keys on key release' chracteristik the ATEN UC10KM shows.

It works now like e.g. the USB native Dell SK-8135 I tested before.

I wonder if beside the geekhack adapter are there other adapters that feature at least a 6KRO?

It's a strange thing, that PS/2 ports are beginning to appear on motherboards again.