If your question is whether p-any's any function and the standard Promise.any function do the same thing, then based on p-any's documentation, yes, they do. They both get fulfilled when the first promise from the iterable gets fulfilled, or get rejected with an AggregateError if all of the promises from the iterable get rejected.
Promise.any is still just a Stage 3 proposal, though it's likely to hit Stage 4 very soon. p-any and similar presumably predate that effort slightly.
This chart (I wish SO's markdown allowed tables!) may be useful for understanding the different Promise combinators:
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| Name | Description | Added In |
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| Promise.allSettled | does not short−circuit | ES2020 |
| Promise.all | short−circuits when an input value is rejected | ES2015 |
| Promise.race | short−circuits when an input value is settled | ES2015 |
| Promise.any | short−circuits when an input value is fulfilled | Stage 3 proposal |
+−−−−−−−−−−−−−−−−−−−−+−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−+
This article the proposal links to may as well.