fix(llm): LiteLLM embed() crashes on model override + finish #1593 review items

[itomek]

Follow-up to #1593 (merged), which added the LiteLLM provider. The claude-bot review on that PR flagged items that merged unaddressed.

Bug (must fix)

LiteLLMProvider.embed() raises TypeError: embedding() got multiple values for keyword argument 'model' whenever a caller overrides the model — model lands in both the explicit model= argument and the spread **call_kwargs. No test currently exercises embed().

Cleanup (bot review)

• Document the litellm provider in docs/sdk/sdks/llm.mdx (Cloud Providers section) — required by the docs policy.
• create_client docstring in src/gaia/llm/factory.py still lists only ("lemonade", "openai", or "claude").
• Redundant drop_params (set globally in __init__ and per-call) — collapse to a single per-call default that callers can override without a duplicate-keyword error.

Scope

src/gaia/llm/providers/litellm.py, src/gaia/llm/factory.py, tests/unit/test_litellm_provider.py, docs/sdk/sdks/llm.mdx. No behavior change to the chat/stream paths.

[github-actions]

Confirmed — this is a real bug, and the diagnosis is spot-on.

In src/gaia/llm/providers/litellm.py, embed() builds call_kwargs = {**self._extra_kwargs, **kwargs} (line 79), then does kwargs.pop("model", self._model) for the explicit model= argument (line 84). The pop targets kwargs, not call_kwargs — so any caller-supplied model stays in the spread and collides with the explicit argument → TypeError: embedding() got multiple values for keyword argument 'model'. The chat() path doesn't hit this because it never spreads model into call_kwargs.

The fix mirrors chat(): resolve the model once and exclude it from the spread, e.g. pop model out before building call_kwargs:

def embed(self, texts: list[str], **kwargs) -> list[list[float]]:
    import litellm

    model = kwargs.pop("model", None) or self._model
    call_kwargs = {**self._extra_kwargs, **kwargs}
    if self._api_key:
        call_kwargs["api_key"] = self._api_key

    response = litellm.embedding(
        model=model,
        input=texts,
        drop_params=True,
        **call_kwargs,
    )
    return [item["embedding"] for item in response.data]

The rest of the cleanup list all checks out against the current code:

• Redundant drop_params — set globally in __init__ (line 27) and per-call (lines 69, 86). Collapsing to the per-call default is the right call; keep it overridable.
• docs/sdk/sdks/llm.mdx — litellm isn't documented in the Cloud Providers section yet; required by the docs policy.
• create_client docstring in src/gaia/llm/factory.py still lists only ("lemonade", "openai", or "claude").

A couple of things for the PR:

• Add an embed() test in tests/unit/test_litellm_provider.py that overrides the model — that's the gap that let this through. Mock litellm.embedding and assert it's called once with the override model and no duplicate kwarg.
• Since this touches an LLM provider path, note in the PR whether any agent's embedding flow actually routes through this provider; if so, an eval run on the affected category is worth a line in the test plan (per CLAUDE.md).

Want to open the PR? Scope is tidy and the four files you listed are exactly right.