fix(websearch): fall back to the request model when a patch carries no model

An empty patched model dispatched a provider-only name instead of falling back, and a
provider-stripped sub-path copied into the patch lost its prefix. A patched model now
keeps its own provider only when its leading segment names one.

litellm/litellm_core_utils/core_helpers.py

@@ -38,15 +38,21 @@ def qualify_provider_stripped_model(model: str, custom_llm_provider: str) -> str
     return f"{custom_llm_provider}/{model}"
 
 
-def qualify_agentic_followup_model(patch_model: str | None, model: str, custom_llm_provider: str) -> str:
-    """Resolve the model an agentic follow-up re-dispatches.
+def names_a_provider(candidate: str) -> bool:
+    """Whether a model name's leading segment is a provider rather than part of the model."""
+    import litellm
+    from litellm.litellm_core_utils.get_llm_provider_logic import is_registered_custom_provider
 
-    A hook that qualified its own patched model owns that choice, including a cross-provider
-    one, so only a bare patched model and the request's provider-stripped model get a prefix.
-    """
-    if patch_model is None:
+    provider_names: Final = {getattr(provider, "value", provider) for provider in litellm.provider_list}
+    return candidate in provider_names or is_registered_custom_provider(candidate)
+
+
+def qualify_agentic_followup_model(patch_model: str | None, model: str, custom_llm_provider: str) -> str:
+    """Resolve the model an agentic follow-up re-dispatches, keeping a hook's own provider."""
+    if not patch_model:
         return qualify_provider_stripped_model(model, custom_llm_provider)
-    if "/" in patch_model:
+    leading_segment: Final = patch_model.split("/", 1)[0]
+    if leading_segment != patch_model and names_a_provider(leading_segment):
         return patch_model
     return qualify_provider_stripped_model(patch_model, custom_llm_provider)
 

tests/unit/litellm_core_utils/test_core_helpers.py

@@ -645,3 +645,12 @@ class TestQualifyAgenticFollowUpModel:
 
     def test_a_patched_model_already_holding_the_request_provider_is_left_alone(self):
         assert qualify_agentic_followup_model("openai/gpt-4o", "gpt-4o", "openai") == "openai/gpt-4o"
+
+    @pytest.mark.parametrize("patched", ["", None])
+    def test_a_patch_without_a_model_falls_back_to_the_request_model(self, patched):
+        assert qualify_agentic_followup_model(patched, "gpt-4o", "openai") == "openai/gpt-4o"
+
+    def test_a_patched_sub_path_model_still_takes_the_request_provider(self):
+        assert qualify_agentic_followup_model("mantle/anthropic.claude-sonnet-5", "gpt-4o", "bedrock") == (
+            "bedrock/mantle/anthropic.claude-sonnet-5"
+        )