Chances are there are other mice that support both protocols on the controller, but use a different USB-PS/2 pin mapping.
My memory suggests that Logitech mice at the time had a PS/2 connector "natively" on the cable that plugs into an adapter for USB. Surely they did the same, skip on any active controller in the adapter and do it all on the controller they already have - those adapters where everywhere, and included with every mouse for a long time, which surely would not have happened if they incurred any meaningful cost pressure.
Now did they use the same mapping? (assuming my memories are not completely wrong anyways) With one being USB-PS/2 and the other PS/2-USB, a test would be stacking both into a noop-adapter USB-USB or PS/2-PS/2 and see if it works.
Sorry I think I was wrong, had an edit open but failed to submit: I believe that I was thinking of keyboards that did the same (in particular of Cherry keyboards), not Logi mice. The same, and for longer I think, because PS/2 held out so much longer in its keyboard variant. At first because of unreliable (or missing?) USB implementation on BIOS level, then because of lingering distrust.
Where PS/2 continued to exist surprisingly long (perhaps still?): the internal connection from laptop mainboard to touchpad. Not the DIN connector, but the protocol. And as a consequence, the cheapest external touchpads (those riding the efficiency of scale of the much higher volume internal market) had been PS/2 for a surprisingly long time.
My memory suggests that Logitech mice at the time had a PS/2 connector "natively" on the cable that plugs into an adapter for USB. Surely they did the same, skip on any active controller in the adapter and do it all on the controller they already have - those adapters where everywhere, and included with every mouse for a long time, which surely would not have happened if they incurred any meaningful cost pressure.
Now did they use the same mapping? (assuming my memories are not completely wrong anyways) With one being USB-PS/2 and the other PS/2-USB, a test would be stacking both into a noop-adapter USB-USB or PS/2-PS/2 and see if it works.