The great rasppberry pi shortage is probably caused by shortages of power electronics and networking chips.
If that was the case the compute modules would be unaffected. You can't get even those right now either.
The compute modules only has a 5V input, which it must convert to the voltages used by the CPU, RAM, peripherals, etc. using aforementioned power ICs. A modern CPU like the BCM2711 usually has several different voltage domains that must be supplied by the PCB designer, ranging from 1.2v to 3.3v.
There is a fab space shortage. The cost to manufacture goes up and so only the highest volume, highest margin chips get made.