Add documentation for remote cluster proxy mode (#52779)

This is related to #49067.

docs/reference/cluster/remote-info.asciidoc

@@ -17,29 +17,47 @@ Returns configured remote cluster information.
 ==== {api-description-title}
 
 The cluster remote info API allows you to retrieve all of the configured
-remote cluster information. It returns connection and endpoint information keyed 
+remote cluster information. It returns connection and endpoint information keyed
 by the configured remote cluster alias.
 
 
 [[cluster-remote-info-api-response-body]]
 ==== {api-response-body-title}
 
-`seeds`::
-	The configured initial seed transport addresses of the remote cluster.
+`mode`::
+    Connection mode for the remote cluster. Returned values are `sniff` and
+    `proxy`.
 
 `connected`::
 	True if there is at least one connection to the remote cluster.
 
-`num_nodes_connected`::
-    The number of connected nodes in the remote cluster.
-
-`max_connections_per_cluster`::
-	The maximum number of connections maintained for the remote cluster.
-
 `initial_connect_timeout`::
 	The initial connect timeout for remote cluster connections.
 
 [[skip-unavailable]]
 `skip_unavailable`::
     Whether the remote cluster is skipped in case it is searched through
     a {ccs} request but none of its nodes are available.
+
+`seeds`::
+    Initial seed transport addresses of the remote cluster when sniff mode is
+    configured.
+
+`num_nodes_connected`::
+    Number of connected nodes in the remote cluster when sniff mode is
+    configured.
+
+`max_connections_per_cluster`::
+    Maximum number of connections maintained for the remote cluster when sniff
+    mode is configured.
+
+`address`::
+    Address for remote connections when proxy mode is configured.
+
+`num_sockets_connected`::
+    Number of open socket connections to the remote cluster when proxy mode
+    is configured.
+
+`max_socket_connections`::
+    The maximum number of socket connections to the remote cluster when proxy
+    mode is configured.

docs/reference/modules/cross-cluster-search.asciidoc

@@ -253,30 +253,33 @@ PUT _cluster/settings
 If `cluster_two` is disconnected or unavailable during a {ccs}, {es} won't
 include matching documents from that cluster in the final results.
 
-[discrete]
-[[ccs-works]]
-== How {ccs} works
-
-include::./remote-clusters.asciidoc[tag=how-remote-clusters-work]
-
 [discrete]
 [[ccs-gateway-seed-nodes]]
-=== Selecting gateway and seed nodes
+== Selecting gateway and seed nodes in sniff mode
 
-Gateway and seed nodes need to be accessible from the local cluster via your
-network.
+For remote clusters using the <<sniff-mode,sniff connection>> mode, gateway and
+seed nodes need to be accessible from the local cluster via your network.
 
-By default, any master-ineligible node can act as a gateway node. If wanted,
-you can define the gateway nodes for a cluster by setting
-`cluster.remote.node.attr.gateway` to `true`.
+By default, any non-<<master-node,master-eligible>> node can act as a
+gateway node. If wanted, you can define the gateway nodes for a cluster by
+setting `cluster.remote.node.attr.gateway` to `true`.
 
 For {ccs}, we recommend you use gateway nodes that are capable of serving as
 <<coordinating-node,coordinating nodes>> for search requests. If
 wanted, the seed nodes for a cluster can be a subset of these gateway nodes.
 
+[discrete]
+[[ccs-proxy-mode]]
+== {ccs} in proxy mode
+
+<<proxy-mode,Proxy mode>> remote cluster connections support {ccs}. All remote
+connections connect to the configured `proxy_address`. Any desired connection
+routing to gateway or <<coordinating-node,coordinating nodes>> must
+be implemented by the intermediate proxy at this configured address.
+
 [discrete]
 [[ccs-network-delays]]
-=== How {ccs} handles network delays
+== How {ccs} handles network delays
 
 Because {ccs} involves sending requests to remote clusters, any network delays
 can impact search speed. To avoid slow searches, {ccs} offers two options for
@@ -300,9 +303,9 @@ low latency.
 +
 See <<ccs-unmin-roundtrips>> to learn how this option works.
 
-[float]
+[discrete]
 [[ccs-min-roundtrips]]
-==== Minimize network roundtrips
+=== Minimize network roundtrips
 
 Here's how {ccs} works when you minimize network roundtrips.
 
@@ -326,9 +329,9 @@ final results in the {ccs} response.
 +
 image:images/ccs/ccs-min-roundtrip-client-response.svg[]
 
-[float]
+[discrete]
 [[ccs-unmin-roundtrips]]
-==== Don't minimize network roundtrips
+=== Don't minimize network roundtrips
 
 Here's how {ccs} works when you don't minimize network roundtrips.