[DOCS] Fix readme links (#1421)

* [DOCS] Fix links in README

* [DOCS] Update link to moved Authentication page

Author: orhantoy

README.md

@@ -80,10 +80,10 @@ We recommend that you write a lightweight proxy that uses this client instead, y
 - [Client configuration](https://www.elastic.co/guide/en/elasticsearch/client/javascript-api/current/client-configuration.html)
 - [API reference](https://www.elastic.co/guide/en/elasticsearch/client/javascript-api/current/api-reference.html)
 - [Breaking changes coming from the old client](https://www.elastic.co/guide/en/elasticsearch/client/javascript-api/current/breaking-changes.html)
-- [Authentication](https://www.elastic.co/guide/en/elasticsearch/client/javascript-api/current/auth-reference.html)
+- [Authentication](https://www.elastic.co/guide/en/elasticsearch/client/javascript-api/current/client-connecting.html#authentication)
 - [Observability](https://www.elastic.co/guide/en/elasticsearch/client/javascript-api/current/observability.html)
-- [Creating a child client](https://www.elastic.co/guide/en/elasticsearch/client/javascript-api/current/child-client.html)
-- [Extend the client](https://www.elastic.co/guide/en/elasticsearch/client/javascript-api/current/extend-client.html)
+- [Creating a child client](https://www.elastic.co/guide/en/elasticsearch/client/javascript-api/current/child.html)
+- [Extend the client](https://www.elastic.co/guide/en/elasticsearch/client/javascript-api/current/extend.html)
 - [Client helpers](https://www.elastic.co/guide/en/elasticsearch/client/javascript-api/current/client-helpers.html)
 - [Typescript support](https://www.elastic.co/guide/en/elasticsearch/client/javascript-api/current/typescript.html)
 - [Testing](https://www.elastic.co/guide/en/elasticsearch/client/javascript-api/current/client-testing.html)