What does it mean that an "embedding model supports queries"? An embedding model maps text to embedding vectors. You can always perform queries with such embedding vectors against a stored set of embeddings.
Which accomplishes the same thing as HyDE, but in the model instead of in text space. If the encoder has a query mode you skip the rewrite.
Voyage has an example of this in `input_type` https://docs.voyageai.com/reference/embeddings-api