I think you are mixing up two different kinds of "32 bit", not surprising really, it's very confusing.
I assume your current image is RGB and shows Image > Mode > 32 bit. This is a special kind of working, not stored in ordinary image files. This is 32 bit per component - 32 bits for red, 32 bits for green and 32 bits for blue. A total, in fact, of 96 bits for each pixel.
Now, when people talk about 32 bit PNG what they mean is it is 32 bits for each pixel: 8 each for red, green and blue and another 8 for "alpha". 24 bit PNG is the same without the alpha. So, if you export to PNG your 32 bits for each component is turned into 8 bits, and when you reopen it that's what you get. This is plenty for delivering graphics to the web. When you reopen a 24 or 32 bits (per pixel) PNG in Photoshop, you'll correctly see that you now have an 8 bit (per component).
Of course, you lose lots of info from your original file, which is why we always save as PSD for editing later.