Document partial search results with skip_unavailable (#84057) (#84299)

This commit adds an explanation for the relation between `allow_partial_search_results` and `skip_unavailable` in CCS requests.

Relates to #33915

Closes #82407

Co-authored-by: James Rodewig <james.rodewig@elastic.co>
(cherry picked from commit 86964c9)

Co-authored-by: Nhat Nguyen <nhat.nguyen@elastic.co>

docs/reference/cluster/remote-info.asciidoc

@@ -41,8 +41,9 @@ by the configured remote cluster alias.
 
 [[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.
+Whether a {ccs} skips the remote cluster if its nodes are unavailable during the
+search. If `true`, a {ccs} also ignores errors returned by the remote cluster.
+Refer to <<skip-unavailable-clusters>>.
 
 `seeds`::
     Initial seed transport addresses of the remote cluster when sniff mode is

docs/reference/search/search-your-data/search-across-clusters.asciidoc

@@ -288,16 +288,29 @@ means the document came from the local cluster.
 
 [discrete]
 [[skip-unavailable-clusters]]
-=== Skip unavailable clusters
+=== Optional remote clusters
 
-By default, a {ccs} returns an error if *any* cluster in the request is
-unavailable.
+By default, a {ccs} fails if a remote cluster in the request returns an
+error or is unavailable. Use the `skip_unavailable` cluster
+setting to mark a specific remote cluster as optional for {ccs}.
 
-To skip an unavailable cluster during a {ccs}, set the
-<<skip-unavailable,`skip_unavailable`>> cluster setting to `true`.
+If `skip_unavailable` is `true`, a {ccs}:
 
-The following <<cluster-update-settings,cluster update settings>> API request
-changes `cluster_two`'s `skip_unavailable` setting to `true`.
+* Skips the remote cluster if its nodes are unavailable during the search. The
+response's `_cluster.skipped` value contains a count of any skipped clusters.
+
+* Ignores errors returned by the remote cluster, such as errors related to
+unavailable shards or indices. This can include errors related to search
+parameters such as <<api-multi-index,`allow_no_indices`>> and
+<<api-multi-index,`ignore_unavailable`>>.
+
+* Ignores the <<search-partial-responses,`allow_partial_search_results`>>
+parameter and the related `search.default_allow_partial_results` cluster setting
+when searching the remote cluster. This means searches on the remote cluster may
+return partial results.
+
+The following <<cluster-update-settings,cluster update settings>>
+API request changes `cluster_two`'s `skip_unavailable` setting to `true`.
 
 [source,console]
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