### Check for existing issues

- [x] I have searched the existing issues and checked that my issue is not a duplicate.

### What happened?

### Summary

Using litellm (SDK / Router) with Snowflake Cortex, I hit a cluster of related issues — some in the `snowflake/` provider code, some in the docs, and some when following the docs' suggestion to use the OpenAI-/Anthropic-compatible Cortex endpoints. Filing together for context; happy to split. Verification status tagged per item (source-checked on `main` 2026-06-18 unless noted).

Background: Snowflake Cortex exposes three REST endpoints — `/api/v2/cortex/inference:complete` (native), `/api/v2/cortex/v1/chat/completions` (OpenAI-compatible), `/api/v2/cortex/v1/messages` (Anthropic-compatible). The litellm `snowflake/` provider only ever targets `inference:complete`.

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### Issue 1 — `snowflake/` drops `tool_calls` when streaming [BUG, verified on main]

`SnowflakeConfig.transform_response` converts Cortex `content_list`/`tool_use` → OpenAI `tool_calls`, but **only for non-streaming**. There is no `get_model_response_iterator` / `chunk_parser`, so streaming inherits the generic `OpenAIGPTConfig` SSE pa…