Clarify the behavior of remote/info and resolve/cluster for connected status of remotes

docs/reference/cluster/remote-info.asciidoc

@@ -25,6 +25,14 @@ The cluster remote info API allows you to retrieve all of the configured
 remote cluster information. It returns connection and endpoint information keyed
 by the configured remote cluster alias.
 
+TIP: This endpoint returns the information that reflects state on the cluster
+you are querying. The `connected` field does not necessarily reflect whether
+the remote cluster is down or unavailable, only whether there is currently an open
+connection to it. Elasticsearch does not spontaneously try to reconnect to a
+disconnected remote cluster. To trigger a reconnection, attempt a
+<<modules-cross-cluster-search,{ccs}>>, <<esql-cross-clusters,{esql} {ccs}>>,
+or try the <<indices-resolve-cluster-api,resolve cluster>> endpoint.
+
 
 [[cluster-remote-info-api-response-body]]
 ==== {api-response-body-title}
@@ -34,7 +42,10 @@ by the configured remote cluster alias.
     `proxy`.
 
 `connected`::
-	True if there is at least one connection to the remote cluster.
+    True if there is at least one open connection to the remote cluster. When
+    false, it means that the cluster no longer has an open connection to the
+    remote cluster. It does not necessarily mean that the remote cluster is
+    down or unavailable, just that at some point a connection was lost.
 
 `initial_connect_timeout`::
 	The initial connect timeout for remote cluster connections.

docs/reference/indices/resolve-cluster.asciidoc

@@ -16,8 +16,9 @@ with this endpoint.
 
 For each cluster in the index expression, information is returned about:
 
-1. whether the querying ("local") cluster is currently connected to each remote cluster
-   in the index expression scope
+1. whether the querying ("local") cluster was able to connect to each remote cluster
+   specified in the index expression. Note that this endpoint actively attempts to
+   contact the remote clusters, unlike the <<cluster-remote-info,remote/info>> endpoint.
 2. whether each remote cluster is configured with `skip_unavailable` as `true` or `false`
 3. whether there are any indices, aliases or data streams on that cluster that match
    the index expression
@@ -112,11 +113,24 @@ deprecated:[7.16.0]
 
 [discrete]
 [[usecases-for-resolve-cluster]]
+=== Test availability of remote clusters
+
+The <<cluster-remote-info,remote/info>> endpoint is commonly used to test whether the "local"
+cluster (the cluster being queried) is connected to its remote clusters, but it does not
+necessarily reflect whether the remote cluster is available or not. The remote cluster may
+be available, while the local cluster is not currently connected to it.
+
+You can use this API to force a reconnection (for example with `GET _resolve/cluster/*:*`) and
+the `connected` field in the response will indicate whether it was successful or not.
+If a connection was (re-)established, this will also cause the
+<<cluster-remote-info,remote/info>> endpoint to now indicate a connected status.
+
+
 === Advantages of using this endpoint before a {ccs}
 
 You may want to exclude a cluster or index from a search when:
 
-1. A remote cluster is not currently connected and is configured with `skip_unavailable`=`false`.
+1. A remote cluster could not be connected to and is configured with `skip_unavailable`=`false`.
 Executing a {ccs} under those conditions will cause
 <<cross-cluster-search-failures,the entire search to fail>>.