I wouldn't say those two are equivalent. A cryptographic hash requires the exact full document to be available to "recover it" from the hash. With a vector embedding you can extract information related to the document from the embedding alone as long as you know (or can guess) what embedding model was used. You won't be able to reconstruct the document but you will be able to infer some meaning from the vector alone
Yes there have been multiple papers showing information extraction from embedding vectors if you know the model used. SHA by design maps similar strings pseud-randomly. Embeddings by design map similar strings similarly.
