I had a similar situation happen to me many years ago when our children were young. My husband's therapist contacted CPS to do a wellness check on our kids. He was a conservative man, a therapist with the veteran's admin and was concerned because my husband had mentioned that we allowed our children to do art work on the walls of our home.
The worker showed up unexpectedly, but she was very kind and non-intrusive. After briefly speaking with the kids and my husband and I, she felt satisfied that the home was safe and left.

I was angry for many years about the CPS intervention. Now, when I look back I'm grateful to know that CPS did take the time and effort to make sure our children were safe in their home.

I'm sorry you have had this added stress. In my experience, it is quite jarring to have a CPS worker suddenly show up at your door. For me, it was also embarrassing.

That said, here are my concerns. You have repeatedly mentioned that you wish you would die. That is terrifying to a child. You might think she doesn't know, but I suspect otherwise.
From the information you've posted here on the forum, you have a severe eating disorder.
You have posted extensively about your concern about your daughter's behavior, and you seem to be quite concerned that you are possibly neglecting her in certain ways.

It sounds to me like your home life right now is extremely pressured. I'm pretty sure that your daughter is absorbing that family stress. I've heard people say that "children are resilient; they will come out okay". Well, that's a nice thought, and possibly a justification, but the truth is that children are usually quiet about whatever is going on in their environment. That does not, however, mean they aren't being profoundly affected.

I believe that CPS was doing their job by making sure your daughter is not in danger, considering the situation. Children come first. That needs to be respected at all times. Most probably, CPS wanted to be sure that your daughter is being properly cared for.