feat: add official Gemini v1beta API routes

Replace /v1/gemini with proper Gemini API paths:
- POST /v1beta/models/{model}:generateContent (sync)
- POST /v1beta/models/{model}:streamGenerateContent (streaming)

Model is extracted from URL path. Uses axum wildcard
catch-all since colons in path segments are not supported.

src/api/mod.rs

@@ -43,7 +43,10 @@ pub fn router(state: Arc<AppState>) -> Router {
             "/v1/chat/completions",
             post(completions::handle_completions),
         )
-        .route("/v1/gemini", post(gemini::handle_gemini))
+        .route(
+            "/v1beta/{*path}",
+            post(gemini::handle_gemini_v1beta),
+        )
         .route("/v1/models", get(handle_models))
         .route("/v1/sessions", get(handle_list_sessions))
         .route("/v1/sessions/{id}", delete(handle_delete_session))
@@ -67,7 +70,8 @@ async fn handle_root() -> Json<serde_json::Value> {
         "endpoints": [
             "/v1/chat/completions",
             "/v1/responses",
-            "/v1/gemini",
+            "/v1beta/models/{model}:generateContent",
+            "/v1beta/models/{model}:streamGenerateContent",
 
             "/v1/models",
             "/v1/sessions",