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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)