Bring-your-own JDK docs improvements (#96404)

- Bury these docs a little more, there's no need for them to be on the landing page for "Set up Elasticsearch".

- Clarify the responsibilities for JDK updates.

docs/reference/setup.asciidoc

@@ -17,22 +17,6 @@ The matrix of officially supported operating systems and JVMs is available here:
 link:/support/matrix[Support Matrix]. Elasticsearch is tested on the listed
 platforms, but it is possible that it will work on other platforms too.
 
-[discrete]
-[[jvm-version]]
-== Java (JVM) Version
-
-Elasticsearch is built using Java, and includes a bundled version of
-https://openjdk.java.net[OpenJDK] from the JDK maintainers (GPLv2+CE)
-within each distribution. The bundled JVM is the recommended JVM and
-is located within the `jdk` directory of the Elasticsearch home directory.
-
-To use your own version of Java, set the `ES_JAVA_HOME` environment variable.
-If you must use a version of Java that is different from the bundled JVM,
-we recommend using a link:/support/matrix[supported]
-https://www.oracle.com/technetwork/java/eol-135779.html[LTS version of Java].
-Elasticsearch will refuse to start if a known-bad version of Java is used.
-The bundled JVM directory may be removed when using your own JVM.
-
 [discrete]
 [[dedicated-host]]
 == Use dedicated hosts

docs/reference/setup/install.asciidoc

@@ -64,6 +64,32 @@ downloaded from the Elastic Docker Registry.
 +
 {ref}/docker.html[Install {es} with Docker]
 
+[discrete]
+[[jvm-version]]
+=== Java (JVM) Version
+
+{es} is built using Java, and includes a bundled version of
+https://openjdk.java.net[OpenJDK] from the JDK maintainers (GPLv2+CE) within
+each distribution. The bundled JVM is the recommended JVM.
+
+To use your own version of Java, set the `ES_JAVA_HOME` environment variable.
+If you must use a version of Java that is different from the bundled JVM, it is
+best to use the latest release of a link:/support/matrix[supported]
+https://www.oracle.com/technetwork/java/eol-135779.html[LTS version of Java].
+{es} is closely coupled to certain OpenJDK-specific features, so it may not
+work correctly with other JVMs. {es} will refuse to start if a known-bad
+version of Java is used.
+
+If you use a JVM other than the bundled one, you are responsible for reacting
+to announcements related to its security issues and bug fixes, and must
+yourself determine whether each update is necessary or not. In contrast, the
+bundled JVM is treated as an integral part of {es}, which means that Elastic
+takes responsibility for keeping it up to date. Security issues and bugs within
+the bundled JVM are treated as if they were within {es} itself.
+
+The bundled JVM is located within the `jdk` subdirectory of the {es} home
+directory. You may remove this directory if using your own JVM.
+
 include::install/targz.asciidoc[]
 
 include::install/zip-windows.asciidoc[]