[Backport 8.8] Update changelog for 8.7 and 8.8 (#1898)

Co-authored-by: Josh Mock <[email protected]>

docs/changelog.asciidoc

@@ -1,6 +1,35 @@
 [[changelog-client]]
 == Release notes
 
+[discrete]
+=== 8.8.0
+
+[discrete]
+==== Features
+
+[discrete]
+===== Support for Elasticsearch `v8.8.0`
+
+You can find all the API changes
+https://www.elastic.co/guide/en/elasticsearch/reference/8.8/release-notes-8.7.0.html[here].
+
+[discrete]
+==== Fixes
+
+[discrete]
+===== Fix type declarations for legacy types with a body key https://github.com/elastic/elasticsearch-js/pull/1784[#1784]
+
+Prior releases contained a bug where type declarations for legacy types that include a `body` key were not actually importing the type that includes the `body` key.
+
+[discrete]
+=== 8.7.0
+
+[discrete]
+===== Support for Elasticsearch `v8.7.0`
+
+You can find all the API changes
+https://www.elastic.co/guide/en/elasticsearch/reference/8.7/release-notes-8.7.0.html[here].
+
 [discrete]
 === 8.6.0