Is it illegal for county to put nanny cams in grandma's home without permission?

I agree there is more to this. But, I would say it's illegal in a private residence especially in private areas.

I have a very hard time believing the county has installed nanny cams in someone’s home. How do you know it was the county that did this?

Well, if the county is investigating suspected elder abuse, they need to watch those places where it might be happening. And bedrooms and bathrooms are going to be on the list.

Is the householder, the actual homeowner, a consenting adult or a vulnerable person? Why has the county been involved in the first place?

Personally, I’d consider it an invasion of privacy. In the bathroom??? Really??? What do they suspect? Is there an APS investigation ongoing? I have the feeling there's a big piece of something missing here in the details.

I would make some noise with whatever Agency is responsible for this and find out if someone, unbeknownst to you, gave permission or what. Just seems really invasive to me.