Support GEMINI_JSON and GEMINI_TOOLS modes with LiteLLM Router

[debu-sinha]

Fixes #1489

What changed

handle_gemini_json and handle_gemini_tools assumed the model is always bound at client creation time (the native Gemini SDK pattern via from_gemini()). When using from_litellm() with a LiteLLM Router, the model is passed at request time in kwargs, which immediately triggered a ConfigurationError.

The fix detects the LiteLLM path by checking if model is present in kwargs:

GEMINI_JSON (LiteLLM path):

• Injects JSON schema instructions into the system message (same as native)
• Sets response_format with type: json_object (OpenAI style, which LiteLLM converts)
• Skips update_gemini_kwargs() since LiteLLM handles message format conversion internally

GEMINI_TOOLS (LiteLLM path):

• Uses OpenAI-style tool definitions and tool_choice (instead of Gemini-specific gemini_schema and tool_config)
• Skips update_gemini_kwargs() for the same reason

The native Gemini SDK path (no model in kwargs) is completely unchanged.

Changes

• instructor/providers/gemini/utils.py: Branch handle_gemini_json and handle_gemini_tools based on whether model is in kwargs. Extract shared schema injection into _inject_json_schema_message helper.
• tests/llm/test_gemini_litellm_compat.py: 13 unit tests covering both GEMINI_JSON and GEMINI_TOOLS through the LiteLLM path, including the exact reproduction from Gemini specific Modes do not work with LiteLLM #1489.

Testing

All 45 tests pass (13 new + 32 existing bedrock):

tests/llm/test_gemini_litellm_compat.py::test_gemini_json_litellm_path_injects_schema PASSED
tests/llm/test_gemini_litellm_compat.py::test_gemini_json_litellm_path_sets_response_format PASSED
tests/llm/test_gemini_litellm_compat.py::test_gemini_json_litellm_path_preserves_model PASSED
tests/llm/test_gemini_litellm_compat.py::test_gemini_json_litellm_path_keeps_openai_message_format PASSED
tests/llm/test_gemini_litellm_compat.py::test_gemini_json_litellm_path_no_response_model PASSED
tests/llm/test_gemini_litellm_compat.py::test_gemini_json_litellm_path_appends_to_existing_system PASSED
tests/llm/test_gemini_litellm_compat.py::test_gemini_json_native_path_no_model PASSED
tests/llm/test_gemini_litellm_compat.py::test_gemini_tools_litellm_path_uses_openai_schema PASSED
tests/llm/test_gemini_litellm_compat.py::test_gemini_tools_litellm_path_sets_tool_choice PASSED
tests/llm/test_gemini_litellm_compat.py::test_gemini_tools_litellm_path_preserves_model PASSED
tests/llm/test_gemini_litellm_compat.py::test_gemini_tools_litellm_path_keeps_openai_message_format PASSED
tests/llm/test_gemini_litellm_compat.py::test_gemini_tools_litellm_path_no_response_model PASSED
tests/llm/test_gemini_litellm_compat.py::test_gemini_json_litellm_router_reproduction PASSED

With this fix, the code from #1489 works as expected:

from litellm import Router
import instructor

router = Router(model_list=[...])
client = instructor.from_litellm(router.completion, mode=instructor.Mode.GEMINI_JSON)

# This now works instead of raising ConfigurationError
response = client.chat.completions.create(
    model="gemini-2.0-flash",
    response_model=PersonalInfo,
    messages=[...],
)