You say "death rate" in the first sentence, but then talk of "death count" and "deaths" in the rest.
Did you mean "death rate" in the rest too? If you meant "death count" or "deaths", then it is not the cast for South Dakota. Their deaths have gone way up per capita over the last few weeks.
There are two big questions most people would like answers too:
1. What are my chances of getting COVID?
2. How screwed am I if I get COVID?
There are a couple of different numbers that can be used for the second.
First, the death rate among people who have COVID can be given. Second, the deaths per capita due to COVID can be given.
If you have the answer to the first, then either form of answer to the second can be computed from the other form of answer.
What's going on in South Dakota is that they are doing very badly on the first half (getting COVID). By "badly" I mean that they make the worst in Florida, back when Florida was the epitome of mishandling COVID, look great.
So even if the death rate among people who have COVID has gone down a little, the deaths per capita has gone way up. The death rate among people with COVID would have to go down way more to offset the way the number of people who get COVID is increasing in South Dakota.