According to E. Kits van Wavern Ps. hydrophila is a synonym of Ps. piluliformis:
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“The here introduced change of name for this well-known species up till now usually called Ps. hydrophila is rather unfortunate, but cannot be avoided….”
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See:
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Kits van Wavern, E. (1985). The Dutch, French, and British Species of Psathyrella. Persoonia Supplement 2. Rijksherbarium: Leiden, Netherlands. 300 p.
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The description starts on page 180.

I agree with P. hydrophila.
I believe P. piluliformis was split from P. hydrophila, but that P. hydrophila and P. piluliformis remain two distinct species.
There remains a lot of confusion between the synonyms and/or separate species.

I’d call them Psathyrella hydrophila here, although the site tells me it should be called something else here. I created and name, and people can vote it out.