Refine phrasing and examples for newly added types

I took a deeper look to double check and adjusted as per my findings

Author: jorbaum

deploy-apps/streaming-logs.html.md.erb

@@ -146,16 +146,22 @@ For example:
 
 ### <a id='health'></a> HEALTH
 
-The Diego Cell emits `HEALTH` logs when running health check actions for an app. These logs are generated by the health check binary that monitors app instances. By default, health check log output is suppressed unless an error occurs.
+The Diego Cell emits `HEALTH` logs for health check activity on an app. This inlcudes lifecycle events as well as monitoring start and health-state transitions.
+
+For example:
+
+<pre class="terminal">
+2026-01-26T13:49:18.72+0000 [HEALTH/0]   OUT Container passed the readiness health check. Container marked ready and added to route pool.
+</pre>
 
 ### <a id='proxy'></a> PROXY
 
-Every app container includes an Envoy sidecar proxy that handles the mTLS handshake with the Gorouter and proxies traffic to the app process. The Envoy sidecar emits `PROXY` logs. By default, Envoy runs with a critical log level, so `PROXY` logs mainly appear when Envoy encounters critical errors, fails to start, or is killed due to the container running out of memory.
+Every app container includes an Envoy sidecar proxy that handles the mTLS handshake with the Gorouter and proxies traffic to the app process. The Envoy sidecar emits `PROXY` logs. By default, Envoy runs with a critical log level, so you rarely see `PROXY` logs. They mainly appear when Envoy exits or is killed, such as when the container runs out of memory.
 
 For example:
 
 <pre class="terminal">
-2026-01-26T13:49:18.72+0000 [PROXY/0]     OUT Exit status 137 (out of memory)
+2026-01-26T13:49:18.72+0000 [PROXY/0]     OUT Exit status 137
 </pre>
 
 
@@ -261,4 +267,4 @@ If you are developing a client that displays a stream of <%= vars.app_runtime_ab
   <br><br>
   By changing the Java log output, you can force your app to reformat stack trace messages, replacing newline
   characters with a token. Set your log parsing code to replace that token with newline characters again to display the
-  logs properly in Kibana.
+  logs properly in Kibana.