I wouldn't really trust correlational studies that link hospital capacity and mortality rate during covid. You want to look for causal studies that try to isolate variation in hospital capacity using some sort of instrument to get to a causal estimate of the increase in capacity on mortality. A lot was going on during the covid pandemic that was probably correlating with hospital overcapacity that will bias the estimates from a correlational study.
Out of curiosity, which mechanism are you thinking about that would lead you to the conclusion that hospital capacity doesn't impact mortality? The story that I have heard the most is that hospitals start to turn away people if they don't have beds from them, leading to either delay in care or no care at all. Both delay or no care lead to higher mortality. I cannot really think of a story where an over-capacity hospital leads to the same or reduced mortality.
If you believe that hospital closures lead to hospital overcapacity or delays in care, you can find some literature that shows that closing hospitals leads to an increase in mortality in the community [1].