feat: add OpenAI Responses API support (POST /v1/responses)

Add full Responses API endpoint alongside existing Chat Completions,
with identical logging/tracking/cost pipeline.

New:
- internal/models/responses.go — request/response/stream types + ToUsage() bridge
- internal/providers/openai_responses.go — OpenAI Responses/ResponsesStream

Modified:
- provider.go — Responses()+ResponsesStream() added to Provider interface
- helpers.go — BuildOpenAIResponsesBody, parsers, SSE stream reader
- circuit_breaker.go — CB wraps Responses, passthrough for stream
- server.go — POST /v1/responses route + handleResponses handler
- all non-OpenAI providers — stub methods with clear error messages

Logging: ResponsesUsage.ToUsage() bridges to models.Usage, feeding same
logRequest() -> DB insert -> dashboard WS -> client stats -> cost calc
pipeline. No schema or logger changes needed.

internal/models/responses.go

@@ -0,0 +1,141 @@
+package models
+
+import "encoding/json"
+
+// Responses API request types
+
+// ResponsesRequest maps to POST /v1/responses body (OpenAI Responses API format).
+// The `input` field can be a string or an array of message objects.
+type ResponsesRequest struct {
+	Model           string          `json:"model"`
+	Input           json.RawMessage `json:"input"` // string or []ResponseInputMessage
+	Instructions    string          `json:"instructions,omitempty"`
+	Temperature     *float64        `json:"temperature,omitempty"`
+	MaxOutputTokens *uint32         `json:"max_output_tokens,omitempty"`
+	TopP            *float64        `json:"top_p,omitempty"`
+	Stream          *bool           `json:"stream,omitempty"`
+	Tools           json.RawMessage `json:"tools,omitempty"`
+	ToolChoice      json.RawMessage `json:"tool_choice,omitempty"`
+	Store           *bool           `json:"store,omitempty"`
+}
+
+// ResponseInputMessage represents a single message in the input array.
+type ResponseInputMessage struct {
+	Role    string          `json:"role"`
+	Content json.RawMessage `json:"content"` // string or []ContentPart
+}
+
+// Responses API response types
+
+// ResponsesResponse maps to OpenAI /v1/responses response.
+type ResponsesResponse struct {
+	ID      string                `json:"id"`
+	Object  string                `json:"object"`
+	Model   string                `json:"model"`
+	Output  []ResponsesOutputItem `json:"output"`
+	Usage   *ResponsesUsage       `json:"usage,omitempty"`
+}
+
+// ResponsesOutputItem represents an item in the output array.
+// For messages: type="message", role, content[].
+// For function calls: type="function_call", id, name, arguments, status.
+type ResponsesOutputItem struct {
+	Type      string                   `json:"type"`
+	Role      string                   `json:"role,omitempty"`
+	Content   []ResponsesOutputContent `json:"content,omitempty"`
+	ID        string                   `json:"id,omitempty"`
+	Name      string                   `json:"name,omitempty"`
+	Arguments string                   `json:"arguments,omitempty"`
+	Status    string                   `json:"status,omitempty"`
+}
+
+// ResponsesOutputContent represents content parts within an output message.
+type ResponsesOutputContent struct {
+	Type        string                   `json:"type"`
+	Text        string                   `json:"text,omitempty"`
+	Annotations []json.RawMessage        `json:"annotations,omitempty"`
+}
+
+// ResponsesUsage maps to the usage block in Responses API.
+type ResponsesUsage struct {
+	InputTokens          uint32                    `json:"input_tokens"`
+	OutputTokens         uint32                    `json:"output_tokens"`
+	TotalTokens          uint32                    `json:"total_tokens"`
+	InputTokensDetails   *ResponsesInputTokensDetails  `json:"input_tokens_details,omitempty"`
+	OutputTokensDetails  *ResponsesOutputTokensDetails `json:"output_tokens_details,omitempty"`
+}
+
+// ResponsesInputTokensDetails maps input token details.
+type ResponsesInputTokensDetails struct {
+	CachedTokens uint32 `json:"cached_tokens"`
+}
+
+// ResponsesOutputTokensDetails maps output token details.
+type ResponsesOutputTokensDetails struct {
+	ReasoningTokens uint32 `json:"reasoning_tokens"`
+}
+
+// ToUsage converts ResponsesUsage to the unified Usage model.
+func (u *ResponsesUsage) ToUsage() *Usage {
+	usage := &Usage{
+		PromptTokens:     u.InputTokens,
+		CompletionTokens: u.OutputTokens,
+		TotalTokens:      u.TotalTokens,
+	}
+	if u.InputTokensDetails != nil && u.InputTokensDetails.CachedTokens > 0 {
+		usage.CacheReadTokens = &u.InputTokensDetails.CachedTokens
+	}
+	if u.OutputTokensDetails != nil && u.OutputTokensDetails.ReasoningTokens > 0 {
+		usage.ReasoningTokens = &u.OutputTokensDetails.ReasoningTokens
+	}
+	return usage
+}
+
+// ResponsesStreamChunk represents an SSE chunk from the Responses streaming endpoint.
+type ResponsesStreamChunk struct {
+	Type   string          `json:"type"`
+	Response *ResponsesStreamPayload `json:"response,omitempty"`
+	Item   *ResponsesStreamPayloadItem `json:"item,omitempty"`
+	Delta  *ResponsesStreamDelta `json:"delta,omitempty"`
+}
+
+// ResponsesStreamPayload represents the "response" field in some SSE chunks.
+type ResponsesStreamPayload struct {
+	Object    string          `json:"object"`
+	ID        string          `json:"id"`
+	Model     string          `json:"model"`
+	Usage     *ResponsesUsage  `json:"usage,omitempty"`
+}
+
+// ResponsesStreamPayloadItem represents the "item" field in SSE chunks.
+type ResponsesStreamPayloadItem struct {
+	Type    string                   `json:"type"`
+	Role    string                   `json:"role,omitempty"`
+	Content []ResponsesOutputContent `json:"content,omitempty"`
+	ID      string                   `json:"id,omitempty"`
+	Name    string                   `json:"name,omitempty"`
+	Status  string                   `json:"status,omitempty"`
+}
+
+// ResponsesStreamDelta represents a content delta in streaming.
+type ResponsesStreamDelta struct {
+	ContentIndex int    `json:"content_index"`
+	Type        string `json:"type"`
+	Text        string `json:"text,omitempty"`
+}
+
+// UnifiedResponsesRequest is the internal unified format for Responses API.
+type UnifiedResponsesRequest struct {
+	ClientID         string
+	Model            string
+	Input            string            // normalized input text
+	InputMessages    []ResponseInputMessage // structured input messages (if provided as array)
+	Instructions     string
+	Temperature      *float64
+	MaxOutputTokens  *uint32
+	TopP             *float64
+	Stream           bool
+	Tools            json.RawMessage
+	ToolChoice       json.RawMessage
+	Store            bool
+}