fix: default stream to false and drop dangling tool_choice (auto-mode classifier)

feat: support Claude Code auto-mode classifier and non-streaming requests

fix: accept system role in messages array

Fix streaming tool calls and input parsing for Responses API

Support more tool types in Responses API (web_search, code_interpreter, etc.)

Add OpenAI Responses API support (/v1/responses endpoint)

Simplify stream converter: direct text streaming, no parsing

Stream text with buffered reasoning: emit thinking first, then stream text

Accumulate text content, emit at finish to avoid splits

Process content before reasoning to avoid chunk splitting

Fix double text block bug by flushing buffer when reasoning field detected

Fix character-by-character output - only buffer for think tags when no reasoning field

Add debug logging for request/response, fix think tag parsing without opening tag

Always parse think tags from content

Fix UTF-8 boundary panic in think tag parsing

Initial Rust port of anthropic-messages-proxy