Update the compatiblity mode section of the docs (#3098)

* Update the compatiblity mode section of the docs

* merge with compatiblity section in index.md

Author: miguelgrinberg

docs/reference/connecting.md

@@ -277,13 +277,6 @@ client = Elasticsearch(
 ```
 
 
-## Enabling the Compatibility Mode [compatibility-mode]
-
-The {{es}} server version 8.0 is introducing a new compatibility mode that allows you a smoother upgrade experience from 7 to 8. In a nutshell, you can use the latest 7.x Python {{es}} {{es}} client with an 8.x {{es}} server, giving more room to coordinate the upgrade of your codebase to the next major version.
-
-If you want to leverage this functionality, please make sure that you are using the latest 7.x Python {{es}} client and set the environment variable `ELASTIC_CLIENT_APIVERSIONING` to `true`. The client is handling the rest internally. For every 8.0 and beyond Python {{es}} client, you’re all set! The compatibility mode is enabled by default.
-
-
 ## Using the Client in a Function-as-a-Service Environment [connecting-faas]
 
 This section illustrates the best practices for leveraging the {{es}} client in a Function-as-a-Service (FaaS) environment.

docs/reference/index.md

@@ -69,8 +69,14 @@ Compatibility does not imply full feature parity. New {{es}} features are suppor
 
 {{es}} language clients are also _backward compatible_ across minor versions — with default distributions and without guarantees. 
 
+### Major version upgrades
+
 :::{tip}
 To upgrade to a new major version, first upgrade {{es}}, then upgrade the Python {{es}} client.
 :::
 
-If you need to work with multiple client versions, note that older versions are also released as `elasticsearch7` and `elasticsearch8`.
+Since version 8.0, the {{es}} server supports a compatibility mode that allows smoother upgrade experiences. In a nutshell, this makes it possible to upgrade the {{es}} server to the next major version, while continuing to use the same client. This gives more room to coordinate the upgrade of your codebase to the next major version.
+
+For example, to upgrade a system that uses {{es}} 8.x you can upgrade the {{es}} server to 9.x first, and the 8.x Python {{es}} client will continue to work (aside from any breaking changes, which should be listed in the server release notes). You can continue using the 8.x client during the server migration, and only upgrade it once the server migration is complete. The process is described in detail in the [REST API compatibility workflow](https://www.elastic.co/docs/reference/elasticsearch/rest-apis/compatibility#_rest_api_compatibility_workflow) section of the {{es}} documentation.
+
+If you need to work with multiple client versions, note that older versions are also released with the `elasticsearch8` and `elasticsearch9` package names so that they can be installed together.