docs(router): split router docs into focused pages (#8122)

Signed-off-by: PeaBrane <yanrpei@gmail.com>

docs/index.yml

@@ -225,8 +225,18 @@ navigation:
         contents:
           - page: Router Guide
             path: components/router/router-guide.md
+          - page: Routing Concepts
+            path: components/router/router-concepts.md
+          - page: Configuration and Tuning
+            path: components/router/router-configuration.md
+          - page: Disaggregated Serving
+            path: components/router/router-disaggregated-serving.md
+          - page: Router Operations
+            path: components/router/router-operations.md
           - page: Router Examples
             path: components/router/router-examples.md
+          - page: Standalone Indexer
+            path: components/router/standalone-indexer.md
           - page: KV Event Replay — Dynamo vs vLLM
             path: components/router/kv-event-replay-comparison.md
       - section: Planner

docs/integrations/kv-events-custom-engines.md

@@ -293,5 +293,5 @@ Stop background tasks (ZMQ listener, event forwarding).
 ## See Also
 
 - **[Event Plane](../design-docs/event-plane.md)**: Transport options (NATS, ZMQ) and configuration
-- **[Router Guide](../components/router/router-guide.md)**: Configuration, tuning, and production setup
+- **[Configuration and Tuning](../components/router/router-configuration.md)**: Router flags, tuning, and production setup
 - **[Router Design](../design-docs/router-design.md)**: Architecture details and event transport modes

docs/observability/metrics.md

@@ -223,7 +223,7 @@ Suppose the backend allows 3 concurrent requests and there are 10 clients contin
 
 The router exposes metrics for monitoring routing decisions and overhead. Defined in `lib/llm/src/kv_router/metrics.rs`.
 
-For router configuration, deployment modes, and tuning, see the [Router Guide](../components/router/router-guide.md).
+For router deployment modes, see the [Router Guide](../components/router/router-guide.md). For router flags and tuning, see [Configuration and Tuning](../components/router/router-configuration.md).
 
 #### Metrics Availability by Configuration