All of that is pre-delta, remember that when COVID first hit in 2020 we still didn't have a good idea how it spread.
The tl;dr is that the US government doesn't do a good job of collecting statistics of how many health care workers died of COVID.
1.5k nursing home workers seems to be the one reliable # from the first article, and The Guardian is saying around 3600 healthcare workers in total.
https://www.statnews.com/2021/10/21/who-estimate-115000-heal...
WHO reports over 100k deaths of healthcare workers world wide.
So statistically a small #, but it doesn't account for the # of nurses who got COVID and had long term symptoms that kept them from going back to work, or who just decided to no longer work at all.
And it looks like these #s are highly biased towards major population centers, so it wasn't an even distribution from the country or anything.