What parts would actually need realtime response? Only thing I can think of would be thrusters, but wouldn't that be solved by an asic? Essentially a network command where you say "I don't care specifically when you do this, but I'm requesting a correction of M-magnitude in this 3-vector. If I don't get an ack within 500ms cancel. "
Navigation / attitude control needs to be real time. Even if there's a microcontroller at the device, the guidance system receives telemetry and then sends commands. If the send is arbitrarily delayed then the resulting motion won't be what the system desired. The microcontroller can't do the complex calculations on its own because it doesn't have all the telemetry from multiple sensors.
Also RTOS tend to have a lot of verification work applied so that you can be confident some facilities just won't fail.
Depending on the complexity of the satellite, a linux node, several linux nodes, or a LOT of linux nodes. Or a very small embedded SoC if your satellite is very simple or has a segregated payload.
If I had barrels full of money to waste, probably a microkernel architecture like fuchsia [1]. The barrels full of money would be turning it into a real time OS. The benefit of such an OS is if there's a bug in the drivers, the kernel itself keeps on plugging along, it can dump and reload the misbehaving driver without crashing.
I'm forgetting the name of it, but there's a special OS designed for space. The main issue is that bits get flipped all the time once you leave the protection of the magnetosphere. On the surface of the earth, we generally trust memory a lot more than you can in space, even with special chips and shielding. It causes all sorts of weird problems and slow-downs.
Commodity equipment running specialized distros of Linux is a growing thing however.