The 99xx chips have two CPU dies, and one cache die is on each CPU die.

IIRC some relatively strange CPUs could run with unbacked cache.

In my case it began with 16K (yes, 161024 bytes) and 90K (yes, 901024 bytes) 5.25" floppy disks (although the floppies were a few months after the computer). Eventually upgraded to 48K RAM and 180K double density floppy disks. The computer: Atari 800.

KolibriOS would fit in there, even with the data in memory. You cannot load it into the cache directly, but when the cache capacity is larger than all the data you read there should be no cache eviction and the OS and all data should end up in the cache more or less entirely. In other words it should be really, really fast, which KolibriOS already is to begin with.