feat: Google (Gemini) provider on the official Gen AI SDK

Phase 4: provider/google on google.golang.org/genai v1.59.0 — lazy cached
client, FunctionResponse tool loop, raw-JSON-schema tools and structured
output, ThinkingLevel reasoning mapping, iter.Pull2 streaming, hermetic
httptest suite via HTTPOptions.BaseURL. Registry wires google + gemini
schemes to the real client; stub machinery deleted (all built-ins real).
ADR-0011; README matrix + CLAUDE.md synced.

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

progress.md

@@ -1,5 +1,21 @@
 # progress
 
+## 2026-06-10 — Phase 4: Google provider (official genai SDK)
+
+**Landed:** `provider/google` on google.golang.org/genai v1.59.0 (ADR-0011):
+lazy cached client (construction never fails; missing key = synthetic 401
+so chains fail over), assistant→model role mapping, FunctionResponse tool
+results with output/error payloads, ParametersJsonSchema raw-schema tools,
+ResponseJsonSchema structured output, ToolChoice→FunctionCallingConfig,
+ReasoningEffort→ThinkingConfig.ThinkingLevel, usage includes thought
+tokens, iter.Pull2-adapted streaming, genai.APIError→llm.APIError mapping.
+Hermetic tests via HTTPOptions.BaseURL + httptest (SSE fixtures for
+streaming). Registry: google + gemini schemes wired to the real provider;
+the last stub machinery deleted — all six built-ins are now real clients.
+README matrix: Google row fully ✅.
+
+**Next:** Phase 5 — Agent run loop, Toolbox ergonomics, Generate[T].
+
 ## 2026-06-10 — Phase 3: REST providers (OpenAI, Anthropic, Ollama×3) + media
 
 **Landed:**