When I look zoomed up, it’s as if the edges of the letters are where the problems are happening. The look like gray pixels and not black.
The grey pixels on the edges of text are normal, (they’re there to make the text look better on your screen). I don’t think it’s the main cause of your blurry prints. But it would certainly yield better prints to have non-pixelated text. The only way to do that is to track down what is causing PS to rasterize it. (Or use layout software that is designed for text instead of raster graphics).