Preserve Responses API reasoning items during tool continuations

Problem

The responses-api backend currently handles response messages and function calls, but drops reasoning output items in both streaming and non-streaming flows. Chat.SupportedItem also has no representation for reasoning items, so manual context replay sends the function call and function_call_output without the reasoning items that accompanied the call.

OpenAI recommends passing reasoning items back with tool outputs for reasoning models, either through previous_response_id or by replaying all relevant output items unchanged. Dropping them can reduce tool-calling quality, increase reasoning-token usage, or break continuation behavior as reasoning support evolves.

Reference: https://developers.openai.com/api/docs/guides/reasoning#keeping-reasoning-items-in-context

Scope

• retain reasoning output items from streaming and non-streaming Responses calls
• preserve item IDs, encrypted content, summaries, and ordering without mutation
• replay relevant reasoning items alongside function calls and function outputs
• keep bounded history, compaction, cancellation, speculative turns, and out-of-band responses correct
• preserve provider-issued function-call IDs needed by exact manual replay

Acceptance criteria

• a Responses turn containing reasoning followed by function_call can accept a matching function_call_output on the next request
• the next request includes the original reasoning and function-call items in their original order
• streaming and non-streaming regression tests cover the complete tool continuation
• existing non-reasoning and OpenAI-compatible provider behavior remains covered