So, grey goo isn't exactly the most useful thing from a military standpoint, not just because of high-entropy and metastable materials that you can't get chemical energy out of, but also that:
Me: Can we have some realistic grey goo at home?
Mom: We already have realistic grey goo at home.
Realistic grey goo at home: Literally just COVID-19
While it's true that this peculiar little thing managed to bring humanity to its knees without trying, I want something that while only brings down "smaller" things like humans and tanks, it does that preferably within seconds or a minute, not months.
Now, "bring down" here means destroying/impeding an object's capability to harm you. So, if the human is in a state where they can't fire their weapon for whatever reason and the tank's main weapon and gun turret becomes inoperable, they've been brought down.
But how are a swarm of micrometre and nanometre robots supposed to be able to quickly disable both organic military personnel and inorganic military hardware?