docs(noxa-9fw.4): describe gemini cli as primary llm backend

- Update CLAUDE.md: provider chain, LLM modules section, CLI examples
- Update env.example: add GEMINI_MODEL, reorder providers (Gemini first)
- Update noxa-llm/src/lib.rs crate doc comment

crates/noxa-llm/src/lib.rs

@@ -1,8 +1,9 @@
-/// noxa-llm: LLM integration with local-first hybrid architecture.
+/// noxa-llm: LLM integration with Gemini-CLI-first hybrid architecture.
 ///
-/// Provider chain tries Ollama (local) first, falls back to OpenAI, then Anthropic.
-/// Provides schema-based extraction, prompt extraction, and summarization
-/// on top of noxa-core's content pipeline.
+/// Provider chain: Gemini CLI (primary) → OpenAI → Ollama → Anthropic.
+/// Gemini CLI requires the `gemini` binary on PATH; GEMINI_MODEL env var sets the model.
+/// Provides schema-validated extraction (with one retry on parse failure),
+/// prompt extraction, and summarization on top of noxa-core's content pipeline.
 pub mod chain;
 pub mod clean;
 pub mod error;