Just had exactly the same problem - dead keyboard and missing driver in 'Devices' on Surface Pro 4.
I tried the 'dead' keyboard on my Surface Pro 6 and it worked fine. I tried my Surface Pro 6 keyboard on the Pro 4 and it failed to be detected.
Hard to say whether it's a Surface Pro 4 hardware error (some sort of failure of the keyboard connector mechanic that stops the keyboard being detected) but it seems to be an issue with older Surface's - Pro 4 and earlier; hence why Microsoft is silent.
This is actually a replacement Surface Pro 4 as the original had the shaky screen issue. Seems devices Pro 5 and newer are a bit more reliable.
I'm going to have to buy a cheap Bluetooth type cover replacement but I'd rather this be fixed if it's just a software issue.
I've just installed 20H2 update and still not detected.