fix(gateway): apply full Claude Code mimicry on /chat/completions and /responses

Before: the OpenAI-compat forwarders only called injectClaudeCodePrompt,
which prepends the Claude Code banner but leaves the rest of the body
in its original non-Claude-Code shape. The codebase already admits this
is insufficient (see the comment on rewriteSystemForNonClaudeCode in
gateway_service.go: "仅前置追加 Claude Code 提示词无法通过检测").

Effect: OAuth accounts served through /v1/chat/completions or /v1/responses
were detected as third-party apps and bled plan quota with:

    Third-party apps now draw from your extra usage, not your plan limits.

Fix:
  - apicompat.AnthropicRequest: add Metadata json.RawMessage so metadata
    survives the OpenAI->Anthropic->Marshal round trip; without it the
    downstream rewrite has no user_id to work with.
  - service: extract applyClaudeCodeOAuthMimicryToBody, a ParsedRequest-free
    variant of the /v1/messages mimicry pipeline
    (rewriteSystemForNonClaudeCode + normalizeClaudeOAuthRequestBody +
    metadata.user_id injection) so the OpenAI-compat forwarders can reuse it.
  - service: add buildOAuthMetadataUserIDFromBody + hashBodyForSessionSeed
    for the same reason (no ParsedRequest at the call site).
  - ForwardAsChatCompletions / ForwardAsResponses: replace the 3-line
    prompt-prepend with the full mimicry pipeline.
  - applyClaudeCodeMimicHeaders: set x-client-request-id per-request
    (real Claude CLI always does); missing/duplicated values are one more
    third-party fingerprint signal.

No change to the native /v1/messages path: it already called the full
pipeline, we only lift those helpers into a reusable function.

Tests:
  - go build ./... passes
  - go test ./internal/service/... ./internal/pkg/apicompat/... passes
  - lsp_diagnostics clean on all touched files
  - pre-existing failures in internal/config are unrelated (env-sensitive
    tests that also fail on upstream main)

backend/internal/pkg/apicompat/types.go

@@ -12,17 +12,23 @@ import "encoding/json"
 
 // AnthropicRequest is the request body for POST /v1/messages.
 type AnthropicRequest struct {
-	Model        string                 `json:"model"`
-	MaxTokens    int                    `json:"max_tokens"`
-	System       json.RawMessage        `json:"system,omitempty"` // string or []AnthropicContentBlock
-	Messages     []AnthropicMessage     `json:"messages"`
-	Tools        []AnthropicTool        `json:"tools,omitempty"`
-	Stream       bool                   `json:"stream,omitempty"`
-	Temperature  *float64               `json:"temperature,omitempty"`
-	TopP         *float64               `json:"top_p,omitempty"`
-	StopSeqs     []string               `json:"stop_sequences,omitempty"`
-	Thinking     *AnthropicThinking     `json:"thinking,omitempty"`
-	ToolChoice   json.RawMessage        `json:"tool_choice,omitempty"`
+	Model       string             `json:"model"`
+	MaxTokens   int                `json:"max_tokens"`
+	System      json.RawMessage    `json:"system,omitempty"` // string or []AnthropicContentBlock
+	Messages    []AnthropicMessage `json:"messages"`
+	Tools       []AnthropicTool    `json:"tools,omitempty"`
+	Stream      bool               `json:"stream,omitempty"`
+	Temperature *float64           `json:"temperature,omitempty"`
+	TopP        *float64           `json:"top_p,omitempty"`
+	StopSeqs    []string           `json:"stop_sequences,omitempty"`
+	Thinking    *AnthropicThinking `json:"thinking,omitempty"`
+	ToolChoice  json.RawMessage    `json:"tool_choice,omitempty"`
+	// Metadata 会被原样透传给上游。OAuth/Claude-Code 路径依赖 metadata.user_id
+	// 参与上游的"是否为官方 Claude Code 请求"判定；如果经由本结构体重新序列化
+	// 时丢弃该字段，网关侧后续的 metadata 重写(ensureClaudeOAuthMetadataUserID/
+	// RewriteUserIDWithMasking) 在 body 里拿不到起点，就无法重建一个合法的
+	// user_id，进而导致请求被归类为第三方 app。
+	Metadata     json.RawMessage        `json:"metadata,omitempty"`
 	OutputConfig *AnthropicOutputConfig `json:"output_config,omitempty"`
 }