feat(responses): route /v1/responses through non-OpenAI adaptors via chat completions conversion

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Summary

Enable channels without native Responses API support (starting with Claude) to serve /v1/responses requests by converting Responses to Chat Completions format, routing through the existing adaptor pipeline, and converting responses back. Any future adaptor (Gemini, Deepseek, etc.) gets support by adding the same 3-line pattern.

Related: #2941, #2043, #1527

Why not use existing PRs directly?

vs #2892 (494 lines, Claude-only)

• Reimplements all logic already in RequestOpenAI2ClaudeMessage (max tokens, thinking, tools, instructions, tool choice)
• Naive SSE passthrough piping raw Claude events without converting to Responses API format. Clients expecting Responses SSE events will not work
• Only works for Claude with no reusable converter for other adaptors
• Adopted from feat(claude): Support calling Claude channels via /v1/responses #2892: the 2-line bug fix for tool calls being dropped when text content exists

vs #2817 (1039 lines)

• Similar adaptor-level approach (good), but includes its own stream state and converter
• Our stream state machine handles additional cases: reasoning content, usage chunks, SummaryIndex field
• Adopted from feat: enhance OpenAI responses handling and compatibility #2817: adaptor-level ConvertOpenAIResponsesRequest pattern, GetJsonType() for input detection, developer to system role mapping, PromptCacheKey/PromptCacheRetention passthrough, non-function tool passthrough via Custom field

Architecture (1006 lines, adaptor-agnostic)

Converters (reusable for any adaptor):

• ResponsesRequestToChatCompletionsRequest: handles developer role mapping, function_call/function_call_output merging into tool messages, content type detection via GetJsonType(), response format conversion, PromptCacheKey/PromptCacheRetention passthrough
• ChatCompletionsResponseToResponsesResponse: non-streaming response conversion
• ChatToResponsesStreamState: streaming state machine emitting proper Responses SSE events (response.created, response.output_text.delta, response.function_call_arguments.delta, response.completed, usage)

Claude adaptor: 3 lines chaining ResponsesRequestToChatCompletionsRequest then ConvertOpenAIRequest (reuses all existing Claude conversion logic)

Files changed

File	Change
relay/channel/claude/adaptor.go	Implement ConvertOpenAIResponsesRequest (+5 lines)
relay/channel/claude/relay-claude.go	Add RelayFormatOpenAIResponses to stream/non-stream handlers
service/openaicompat/responses_to_chat.go	Add converters + bug fix from #2892
service/openaicompat/chat_stream_to_responses_stream.go	New: reusable stream state machine
service/openai_chat_responses_compat.go	Service wrapper functions
dto/openai_response.go	Add fields to ResponsesStreamResponse

Test plan

• Streaming /v1/responses through Claude channel (verify SSE events match Responses API format)
• Non-streaming /v1/responses through Claude channel
• Tool calls with text content (both appear in output)
• Multi-turn with function_call + function_call_output in input

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Addressed remaining CodeRabbit feedback:

• encoding/json import: Replaced all json.RawMessage with []byte in both responses_to_chat.go and chat_stream_to_responses_stream.go, removed direct encoding/json imports.
• input_file key lookup: Changed partMap["file"] to partMap["file_data"] to match the Responses API spec.
• Tool-call Content nil: Changed Content: "" to Content: nil in flushToolCalls so tool-call-only messages serialize as "content": null.
• Reasoning output index: Allocated via NextOutputIndex instead of hardcoded 0 to avoid colliding with message/tool output indices.
• Reasoning done event: Added response.reasoning_summary_text.done emission in FinalEvents so reasoning streams have a proper closing event.