[Docs] Add breaking change to release notes (#200065)

## Summary

Adding a Kibana-related breaking change found in the Security release
notes.

docs/CHANGELOG.asciidoc

@@ -156,9 +156,22 @@ The Observability AI Assistant specific advanced setting for Logs index patterns
 //*Impact* +
 //!!TODO!!
 ====
-
 
-
+[float]
+[[breaking-changes-8.16.0]]
+=== Breaking changes
+
+Breaking changes can prevent your application from optimal operation and performance.
+Before you upgrade to 8.16.0, review the breaking changes, then mitigate the impact to your application.
+
+[discrete]
+.Updated request processing during shutdown.
+[%collapsible]
+====
+*Details* +
+During shutdown, {kib} now waits for all the ongoing requests to complete according to the `server.shutdownTimeout` setting. During that period, the incoming socket is closed and any new incoming requests are rejected. Before this update, new incoming requests received a response with the status code 503 and body `{"message": "Kibana is shutting down and not accepting new incoming requests"}`. For more information, refer to {kibana-pull}180986[#180986].
+==== 
+
 [float]
 [[features-8.16.0]]
 === Features

docs/upgrade-notes.asciidoc

@@ -434,6 +434,15 @@ The endpoint is now split into two separate endpoints:
 
 // General settings
 
+[discrete]
+[[breaking-180986]]
+.[General settings] Updated request processing during shutdown. (8.16)
+[%collapsible]
+====
+*Details* +
+During shutdown, {kib} now waits for all the ongoing requests to complete according to the `server.shutdownTimeout` setting. During that period, the incoming socket is closed and any new incoming requests are rejected. Before this update, new incoming requests received a response with the status code 503 and body `{"message": "Kibana is shutting down and not accepting new incoming requests"}`. For more information, refer to {kibana-pull}180986[#180986].
+====
+
 [discrete]
 [[breaking-111535]]
 .[General settings] Removed `CONFIG_PATH` and `DATA_PATH` environment variables. (8.0)