[DISCUSSION-54853] Update webserver probe health check doc (#59942)

* [DISCUSSION-54853] Update webserver probe health check doc

* Remove empty line before health check note

* fix indentation on docs

Author: hanxdatadog

airflow-core/docs/administration-and-deployment/logging-monitoring/check-health.rst

@@ -36,7 +36,7 @@ Webserver Health Check Endpoint
 -------------------------------
 
 To check the health status of your Airflow instance, you can simply access the endpoint
-``/api/v2/monitor/health``. It will return a JSON object in which a high-level glance is provided.
+``/api/v2/monitor/health``. It will return a JSON object that provides a high-level glance at the health status across multiple Airflow components.
 
 .. code-block:: JSON
 
@@ -86,9 +86,12 @@ Served by the web server, this health check endpoint is independent of the newer
 
 .. note::
 
-  For this check to work, at least one working web server is required. Suppose you use this check for scheduler
-  monitoring, then in case of failure of the web server, you will lose the ability to monitor scheduler, which means
-  that it can be restarted even if it is in good condition. For greater confidence, consider using :ref:`CLI Check for Scheduler <check-health/cli-checks-for-scheduler>` or  :ref:`Scheduler Health Check Server <check-health/scheduler-health-check-server>`.
+  * For this check to work, at least one working web server is required. Suppose you use this check for scheduler
+    monitoring, then in case of failure of the web server, you will lose the ability to monitor scheduler, which means
+    that it can be restarted even if it is in good condition. For greater confidence, consider using :ref:`CLI Check for Scheduler <check-health/cli-checks-for-scheduler>` or  :ref:`Scheduler Health Check Server <check-health/scheduler-health-check-server>`.
+
+  * Using this endpoint as webserver probes (liveness/readiness) makes it contingent on Airflow core components' availability (database, scheduler, etc).
+    Webservers will be frequently restarted if any of these core components are down. To make Webservers less prone to other components' failures, consider using endpoints like ``api/v2/version``.
 
 .. _check-health/scheduler-health-check-server: