Remove references from a few more places

docs/developer/advanced/running-elasticsearch.asciidoc

@@ -76,7 +76,6 @@ If many other users will be interacting with your remote cluster, you'll want to
 [source,bash]
 ----
 kibana.index: '.{YourGitHubHandle}-kibana'
-xpack.task_manager.index: '.{YourGitHubHandle}-task-manager-kibana'
 ----
 
 ==== Running remote clusters

docs/settings/task-manager-settings.asciidoc

@@ -22,9 +22,6 @@ Task Manager runs background tasks by polling for work on an interval.  You can
 | `xpack.task_manager.request_capacity`
   | How many requests can Task Manager buffer before it rejects new requests.  Defaults to 1000.
 
-| `xpack.task_manager.index`
-  | The name of the index used to store task information.  Defaults to `.kibana_task_manager`.
-
   | `xpack.task_manager.max_workers`
   | The maximum number of tasks that this Kibana instance will run simultaneously.  Defaults to 10.
     Starting in 8.0, it will not be possible to set the value greater than 100.

docs/user/production-considerations/task-manager-production-considerations.asciidoc

@@ -12,7 +12,7 @@ This has three major benefits:
 
 [IMPORTANT]
 ==============================================
-Task definitions for alerts and actions are stored in the index specified by <<task-manager-settings, `xpack.task_manager.index`>>. The default is `.kibana_task_manager`.
+Task definitions for alerts and actions are stored in the index `.kibana_task_manager`.
  
 You must have at least one replica of this index for production deployments.
 

src/dev/build/tasks/os_packages/docker_generator/resources/base/bin/kibana-docker

@@ -395,7 +395,6 @@ kibana_vars=(
     xpack.spaces.enabled
     xpack.spaces.maxSpaces
     xpack.task_manager.enabled
-    xpack.task_manager.index
     xpack.task_manager.max_attempts
     xpack.task_manager.max_poll_inactivity_cycles
     xpack.task_manager.max_workers