i'm not an expert but i think the word expansion here is referring to techniques they use to spread everything out in order to make it easier to see. someone told me that they use the same material that baby diapers are made out of which expands when you soak it in water.
Yes, sodium polyacrylate is used in both expansion microscopy and baby diapers.
However you also need a few other ingredients to ensure isotropic expansion, or otherwise the expanded sample isn't scaled uniformly in all axis and you get a skewed view of the sample.