The short version of this answer boils down to something pretty simple and easy:
Cheap, easy: try more different keyboards with your passive PS/2↔USB pin adapter
Not cheap, still easy: buy a really expensive, nice keyboard that also works over PS/2 and take it as an excuse to get yourself a nice keyboard for day-to-day computing!
The passive PS/2↔USB pin adapters not working may be merely a factor of your choice of USB keyboard to be converted being too new.
If you have that many more USB keyboards stashed away, it might be worth trying the adapter on several different keyboards based on a few key factors.
I'll try and communicate what I've noticed about this stuff as best I can. These aren't hard and fast rules for finding a PS/2 adaptable keyboard, as much as a short gist of guidelines that can hopefully point you at a compatible keyboard in your spare parts pile.
In the below image, take notice of the styling of both the meta/"Windows" key - a flat modern icon of Microsoft's recent motifs, and the OEM Dell branding - indicating this keyboard likely came bundled as part of desktop system. Both of these points would suggest this keyboard is probably too new to utilize a multi-mode controller IC. Lacking a multi-mode controller IC, this keyboard would be incapable of detecting when it was plugged in to a PS/2 port with a passive pin adapter and would lack the internal logic circuitry to enable to function as anything but a USB keyboard.
It also features an thematically darkened aesthetic common to a newer era of consumer computer hardware - probably the loudest indicator of a keyboard's age outside of chiclet keycaps.
Supposing you have enough old USB keyboards around, finding one that's closer to the era of when PS/2 devices were still popular may allow the use of one of these passive adapters.
In the image below, it can be seen that this keyboard features an older styling overall. The icon on the "Windows key" hails from the increasingly distant era of Microsoft's Windows Vista design motifs - an OS at it's prime in a time when PS/2 hardware was still in style. The OEM Logitech indicates this keyboard is more generic than the Dell (or HP, Acer, etc...), and was probably purchased discretely for use with any given desktop system of the time. This keyboard also features a thematically lighter aesthetic that comes from a remarkably obsolete era of computing. These points don't add up to guarantee a cross compatible keyboard, but are positive indicators in that direction. This is a keyboard more likely to have a multi-mode controller IC which would function with the typical passive PS/2↔USB pin adapter.
The second linked image could easily be a better example, but still illustrates the point.
If you absolutely need a different but specifically PS/2 keyboard at the end of the day, good 'ol ebay tends to be an acceptable place to check. In between all the random and poorly priced stuff one can sometimes find some good deals. Please note, the above link is not in any way an endorsement of the listing or seller (and indeed I expect it to be well expired by the time this question is in google results for anything), but a mere example of the point.
It may also bear worth reframing of the problem as an opportunity to buy a nice buckling spring Model M keyboard - they came in PS/2 natively back in the day, and are within the ballpark of $100-200AUD depending on various factors. If my understanding serves me, unicomp and cherry may also have some PS/2 compatible keyboards available which are generally well regarded. I would also not be surprised to learn of any modern "gaming" oriented keyboards on the market that have snuck a PS/2-compatible mode into their controller IC for use with the passive adapters, but that's far more web research than fits the scope of this answer.