PS/2 uses a Bi-Directional, Synchronous, Serial protocol that is much simpler than the USB protocol which must negotiate the protocol, Identify that the device is a HID (Human Interface Device), and then move the data. USB to PS2 Keyboard and Mouse Adapter for - Compare prices of 42144 products in Cables and Connectors from 153 Online Stores in Australia. Here is a link to a PS/2 keyboard for <$7 US. I would look for a PS/2 keyboard or an older model USB keyboard that might have the needed firmware or just buy a PS/2 keyboard. The 4XEM PS/2 Keyboard to USB Adapter features a durable 6-Pin (PS/2) Female connection to a USB-A Male connection, allowing you to connect a PS/2 keyboard. Many older USB keyboards did that but newer models may use chips that don't contain the code needed to output a PS/2 signal and thus will not work with passive PS/2 adapters. It is true if the keyboard or mouse is designed to detect if it is connected to PS/2 or USB ports and adjust the signalling.

Because those adapters don't do anything to change the signals, it just changes the physical pins, I think it's up to the keyboard to realize 'oh, I'm plugged into a PS/2 port, I need to send PS/2 signals now' and maybe some keyboards don't support that anymore? Did you try that USB->PS2 adapter directly on a desktop? Because I wonder if it's just a problem with the keyboard.

Usb to ps2 converter for mouse