The right image is not in sRGB, it's in Display P3. The difference in reds is pretty subtle, so most likely if Paint.NET is showing a dramatic difference, it's misinterpreting the color space of the PNG image.
Because Chrome and FF smash the color information in the bitmap into 32-bit integer sRGB format instead of a 128-bit float format with a color space.
Do you have color management fully enabled in Firefox? If you don't have a color profile assigned then Firefox will probably just treat your screen as sRGB, meaning that both images will be compressed into the tiny sRGB gamut and look the same.
I'm not sure how / whether Paint.NET does color management.
In both Firefox and Chrome I couldn't see the webkit logo on the right hand red square, HOWEVER if I copy/pasted the right hand red square into Paint.NET the logo was VERY visible. Why did it work in one app and not the others?