docs: clean up databases intro page

#7221

docs/docs/getting-started/databases.md

@@ -4,15 +4,11 @@ title: Databases
 
 Auth.js offers multiple database adapters. Check our guides on:
 
-- [using a database adapter](/guides/adapters/using-a-database-adapter)
-- [creating your own](/guides/adapters/creating-a-database-adapter)
-
-> As of **v4** Auth.js no longer ships with an adapter included by default. If you would like to persist any information, you need to install one of the many available adapters yourself. See the individual adapter documentation pages for more details.
+- [Using a database adapter](/guides/adapters/using-a-database-adapter)
+- [Creating your own](/guides/adapters/creating-a-database-adapter)
 
 To learn more about databases in Auth.js and how they are used, check out [databases in the FAQ](/concepts/faq#databases).
 
----
-
 ## How to use a database
 
-See the [documentation for adapters](/reference/adapters/overview) for more information on advanced configuration, including how to use Auth.js with other databases using a [custom adapter](/guides/adapters/creating-a-database-adapter).
+See the [documentation for adapters](/reference/adapters) for more information on advanced configuration, including how to use Auth.js with other databases using a [custom adapter](/guides/adapters/creating-a-database-adapter).