Update the compatiblity mode section of the docs

Author: miguelgrinberg

docs/reference/connecting.md

@@ -277,12 +277,11 @@ client = Elasticsearch(
 ```
 
 
-## Enabling the Compatibility Mode [compatibility-mode]
+## Version Compatibility [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.
+Since version 8.0, the {{es}} server supports a compatibility mode that allows smoother upgrade experiences. In a nutshell, this makes it possible to use an older Python {{es}} client with a newer {{es}} server, giving 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 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.
 
 ## Using the Client in a Function-as-a-Service Environment [connecting-faas]