docs: add docs explaining graceful shutdown (envoyproxy#6729)

* docs: add docs explaining graceful shutdown

fixes: envoyproxy#2686

Signed-off-by: Arko Dasgupta <arko@tetrate.io>

Author: arkodg

site/content/en/latest/tasks/operations/graceful-shutdown.md

@@ -0,0 +1,91 @@
+---
+title: "Graceful Shutdown and Hitless Upgrades"
+---
+
+Envoy Gateway enables zero-downtime deployments through graceful connection draining during pod termination.
+
+## Overview
+
+The shutdown manager sidecar coordinates graceful connection draining during pod termination, providing:
+
+- Zero-downtime rolling updates
+- Configurable drain timeouts
+- Automatic health check failure to remove pods from load balancer rotation
+
+### Shutdown Process
+
+1. Kubernetes sends SIGTERM to the pod
+2. Shutdown manager fails health checks via `/healthcheck/fail`
+   - This causes Kubernetes readiness probes to fail
+   - External load balancers and services stop routing new traffic to the pod
+   - Existing connections continue to be served while draining
+3. Connection monitoring begins, polling `server.total_connections`
+4. Process exits when connections reach zero or drain timeout is exceeded
+
+## Configuration
+
+Graceful shutdown behavior includes default values that can be overridden using the EnvoyProxy resource. The EnvoyProxy resource can be referenced in two ways:
+1. **Gateway-level**: Referenced from a Gateway via `infrastructure.parametersRef`
+2. **GatewayClass-level**: Referenced from a GatewayClass via `parametersRef`
+
+**Default Values:**
+- `drainTimeout`: 60 seconds - Maximum time for connection draining
+- `minDrainDuration`: 10 seconds - Minimum wait before allowing exit
+
+{{< tabpane text=true >}}
+{{% tab header="Gateway-Level Configuration" %}}
+
+```yaml
+apiVersion: gateway.networking.k8s.io/v1
+kind: Gateway
+metadata:
+  name: eg
+spec:
+  gatewayClassName: eg
+  infrastructure:
+    parametersRef:
+      group: gateway.envoyproxy.io
+      kind: EnvoyProxy
+      name: graceful-shutdown-config
+  listeners:
+  - name: http
+    port: 80
+    protocol: HTTP
+---
+apiVersion: gateway.envoyproxy.io/v1alpha1
+kind: EnvoyProxy
+metadata:
+  name: graceful-shutdown-config
+spec:
+  shutdown:
+    drainTimeout: "90s"      # Override default 60s
+    minDrainDuration: "15s"  # Override default 10s
+```
+
+{{% /tab %}}
+{{% tab header="GatewayClass-Level Configuration" %}}
+
+```yaml
+apiVersion: gateway.networking.k8s.io/v1
+kind: GatewayClass
+metadata:
+  name: eg
+spec:
+  controllerName: gateway.envoyproxy.io/gatewayclass-controller
+  parametersRef:
+    group: gateway.envoyproxy.io
+    kind: EnvoyProxy
+    name: graceful-shutdown-config
+---
+apiVersion: gateway.envoyproxy.io/v1alpha1
+kind: EnvoyProxy
+metadata:
+  name: graceful-shutdown-config
+spec:
+  shutdown:
+    drainTimeout: "90s"      # Override default 60s
+    minDrainDuration: "15s"  # Override default 10s
+```
+
+{{% /tab %}}
+{{< /tabpane >}}