Why does SIMPER analysis produce incorrect p-values depending on which R and package versions are used?

Github has some illuminating commits in vegan's history.

vegan::simper underwent a significant rewrite (or actually changed defaults to a different internal function) at some point between v2.5.7 and v2.6.4 -- see here. They mention "The results are identical to the old one within floating-point precision" which didn't turn out to be true in your specific case.

And then you have this commit whose message should tell you all you need to know: "arbitrary p-values were reported for missing species: now NA". It also references a now-deleted Stack Overflow discussion that had "vegan-simper-analysis-producing-incorrect-p-values" in its URL.

In summary: it's almost certainly a bug in vegan::simper that was introduced after v2.5.7 and should have been fixed since v2.7.2.