[Claude Code - Stage 2] Server-side gateway tool loop for Messages

[ashwing]

Part of #113 (Claude Code integration). This is the core value-add.

When the model emits a gateway-owned tool_use (web_search, MCP), the gateway must execute it server-side and continue the loop — never handing it back to Claude Code. The spike proved this is the only mechanism that works: Claude Code errors on any tool it didn't declare, so gateway tools must stay invisible to the client (see #98 → Verification).

Scope:

• Map Anthropic tool_use/tool_result content blocks to the shared tool framework's gateway-owned vs. client-owned classification.
• Run the hide-the-call loop (run_until_gateway_tools_complete, landed in refactor: drive gateway tool loop with LoopDecision (PR B) #83) on the Messages path: inject the gateway tool into the upstream call only, execute it, append the tool_result, loop, surface only the final assistant message.
• Emit correct Anthropic SSE for surfaced calls and suppress hidden gateway calls (reuses the existing emit_gateway_*_events logic on main; keep block index contiguous).
• Handle parallel tool_use, the full stop_reason set (incl. pause_turn), and streaming input_json_delta args.
• Record the acceptance cassette — the upstream Messages turns (turn 0: model emits the gateway tool_use; turn 1: final text after the tool_result) so the loop is covered hermetically in CI, not only live. This records the upstream side, so it reuses the test: record real gateway tool loop cassettes (OpenAI + vLLM) #94 recorder pattern and doesn't depend on the loop existing — it can start immediately. May need a small recorder change for the Messages response shape.
• Acceptance test: a real gateway-owned web_search turn completes end-to-end through /v1/messages with the tool hidden from the client, replayed from that cassette.

Dependency: the shared loop is currently typed to RequestPayload/ResponsePayload; Stage 2's clean form needs it factored to an API-agnostic shape. That factoring is owned by the pending Layering ADR (tool-framework.md Future Work), so this should sequence after / alongside that decision, not reshape the core unilaterally. (The cassette recording sub-task above has no such dependency and can begin right away.)

Happy to take this one.