[Examples] Resettle Observability examples. (#40123)

Signed-off-by: wang.yuqi <yuqi.wang@daocloud.io>

docs/design/metrics.md

@@ -42,7 +42,7 @@ These are documented under [Inferencing and Serving -> Production Metrics](../us
 
 ### Grafana Dashboard
 
-vLLM also provides [a reference example](../../examples/online_serving/prometheus_grafana/README.md) for how to collect and store these metrics using Prometheus and visualize them using a Grafana dashboard.
+vLLM also provides [a reference example](../../examples/observability/prometheus_grafana/README.md) for how to collect and store these metrics using Prometheus and visualize them using a Grafana dashboard.
 
 The subset of metrics exposed in the Grafana dashboard gives us an indication of which metrics are especially important:
 
@@ -657,7 +657,7 @@ vLLM has support for OpenTelemetry tracing:
 - Added by <https://github.com/vllm-project/vllm/pull/4687> and reinstated by <https://github.com/vllm-project/vllm/pull/20372>
 - Configured with `--oltp-traces-endpoint` and `--collect-detailed-traces`
 - [OpenTelemetry blog post](https://opentelemetry.io/blog/2024/llm-observability/)
-- [User-facing docs](../../examples/online_serving/opentelemetry/README.md)
+- [User-facing docs](../../examples/observability/opentelemetry/README.md)
 - [Blog post](https://medium.com/@ronen.schaffer/follow-the-trail-supercharging-vllm-with-opentelemetry-distributed-tracing-aa655229b46f)
 - [IBM product docs](https://www.ibm.com/docs/en/instana-observability/current?topic=mgaa-monitoring-large-language-models-llms-vllm-public-preview)
 

examples/online_serving/dashboards/README.md → examples/observability/dashboards/README.md

@@ -74,8 +74,8 @@ percli apply -f perses/performance_statistics.yaml
 
 For detailed deployment instructions and platform-specific options, see:
 
-- **[Grafana Documentation](./grafana)** - JSON dashboards, operator usage, manual import
-- **[Perses Documentation](./perses)** - YAML specs, CLI usage, operator wrapping
+- **[Grafana Documentation](grafana)** - JSON dashboards, operator usage, manual import
+- **[Perses Documentation](perses)** - YAML specs, CLI usage, operator wrapping
 
 ## Contributing