feat(server): API relay gateway backend M0-M4

Gin + GORM + pure-Go SQLite. Users/auth (JWT), API key management with
quotas, proxy gateway with weighted channel failover and health checks,
usage/billing ledger, cross-protocol conversion (Anthropic Messages /
OpenAI Chat Completions / OpenAI Responses), and channel/model admin API.
Channels declare native API formats and auto-convert the rest.

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>

server/internal/proxy/responses/types.go

@@ -0,0 +1,42 @@
+package responses
+
+import "encoding/json"
+
+// Request is an OpenAI Responses API request. The gateway only needs the
+// model + stream fields for routing; the full body passes through raw.
+type Request struct {
+	Model           string          `json:"model"`
+	Stream          bool            `json:"stream"`
+	Instructions    json.RawMessage `json:"instructions"`
+	Input           json.RawMessage `json:"input"`
+	MaxOutputTokens *int            `json:"max_output_tokens"`
+	PreviousResponseID string       `json:"previous_response_id"`
+	Tools           json.RawMessage `json:"tools"`
+	Reasoning       json.RawMessage `json:"reasoning"`
+	Text            json.RawMessage `json:"text"`
+	OutputFormat    json.RawMessage `json:"output_format"`
+}
+
+// Response is the non-stream Responses response.
+type Response struct {
+	ID       string       `json:"id"`
+	Object   string       `json:"object"`
+	Created  int64        `json:"created"`
+	Model    string       `json:"model"`
+	Status   string       `json:"status"`
+	Output   json.RawMessage `json:"output"`
+	Usage    *Usage       `json:"usage,omitempty"`
+}
+
+type Usage struct {
+	InputTokens          int64 `json:"input_tokens"`
+	OutputTokens         int64 `json:"output_tokens"`
+	TotalTokens          int64 `json:"total_tokens"`
+	InputTokensDetails   UsageDetails `json:"input_tokens_details,omitempty"`
+	OutputTokensDetails  UsageDetails `json:"output_tokens_details,omitempty"`
+}
+
+type UsageDetails struct {
+	CachedTokens int64 `json:"cached_tokens,omitempty"`
+	ReasoningTokens int64 `json:"reasoning_tokens,omitempty"`
+}