fix(inference): enable routing of models with provider_data alone (backport #3928) (#4142)

This PR enables routing of fully qualified model IDs of the form
`provider_id/model_id` even when the models are not registered with the
Stack.

Here's the situation: assume a remote inference provider which works
only when users provide their own API keys via
`X-LlamaStack-Provider-Data` header. By definition, we cannot list
models and hence update our routing registry. But because we _require_ a
provider ID in the models now, we can identify which provider to route
to and let that provider decide.

Note that we still try to look up our registry since it may have a
pre-registered alias. Just that we don't outright fail when we are not
able to look it up.

Also, updated inference router so that the responses have the _exact_
model that the request had.

## Test Plan

Added an integration test

Closes #3929<hr>This is an automatic backport of pull request #3928 done
by [Mergify](https://mergify.com).

---------

Co-authored-by: Ashwin Bharambe <ashwin.bharambe@gmail.com>
Co-authored-by: ehhuang <ehhuang@users.noreply.github.com>

llama_stack/providers/utils/inference/embedding_mixin.py

@@ -46,8 +46,7 @@ class SentenceTransformerEmbeddingMixin:
             raise ValueError("Empty list not supported")
 
         # Get the model and generate embeddings
-        model_obj = await self.model_store.get_model(params.model)
-        embedding_model = await self._load_sentence_transformer_model(model_obj.provider_resource_id)
+        embedding_model = await self._load_sentence_transformer_model(params.model)
         embeddings = await asyncio.to_thread(embedding_model.encode, input_list, show_progress_bar=False)
 
         # Convert embeddings to the requested format

llama_stack/providers/utils/inference/openai_mixin.py

@@ -201,8 +201,11 @@ class OpenAIMixin(NeedsRequestProviderData, ABC, BaseModel):
         :param model: The registered model name/identifier
         :return: The provider-specific model ID (e.g., "gpt-4")
         """
-        # Look up the registered model to get the provider-specific model ID
         # self.model_store is injected by the distribution system at runtime
+        if not await self.model_store.has_model(model):  # type: ignore[attr-defined]
+            return model
+
+        # Look up the registered model to get the provider-specific model ID
         model_obj: Model = await self.model_store.get_model(model)  # type: ignore[attr-defined]
         # provider_resource_id is str | None, but we expect it to be str for OpenAI calls
         if model_obj.provider_resource_id is None: