There's two ways microcode goes on Intel CPUs. The first is when it gets flashed in at the factory onto an OTP ROM. The second is when it gets uploaded to a block of internal RAM by your computer, every time it boots. That's why packages like this one (https://www.archlinux.org/packages/extra/any/intel-ucode/) exist.
One is set at the factory, one is set by your computer every time, once at boot, before the completion of boot. Also, it's very carefully signed, so even if you managed to put a bootkit before the OS boot, you would need to steal Intel's microcode key.
Microcode is not targetable. Few things at that level are. (A decent example of something that might be more targetable at that level is a hard drive controller. Less difficult but still not easy.) The amount of engineering needed to pull off an exploit that is "99.9% chance" unnoticeable, but still persistent, is much more than that of a "99% chance".
(I know nothing of AMD's CPUs and their microcode, but I'm guessing it's much of the same.)