backlog: follow up on search provider config

[Pouyanpi]

1. It feels a bit wrong for an object to mutate its data object passed in during initialization. I'd prefer to handle this at the Pydantic validation stage.
2. Some embedding models (Gemini) have a dimensionality value in embedding_parameters which we'd need to add to item hash. Without this if a users changes the dimensionality we won't invalidate the cache and cause errors.

Originally posted by @tgasser-nv in #1753 (review)