docs: File extension named processor deprecation

docs/src/extend/custom-processors.md

@@ -139,6 +139,12 @@ See [Specify a Processor](../use/configure/plugins#specify-a-processor) in the P
 
 ## File Extension-named Processor
 
+::: warning
+This feature is deprecated and only works in eslintrc-style configuration files. Flat config files do not automatically apply processors; you need to explicitly set the `processor` property.
+
+**From ESLint v9.0.0+, this feature will be removed.**
+:::
+
 If a custom processor name starts with `.`, ESLint handles the processor as a **file extension-named processor**. ESLint applies the processor to files with that filename extension automatically. Users don't need to specify the file extension-named processors in their config files.
 
 For example:

docs/src/extend/plugins.md

@@ -89,6 +89,12 @@ Plugin environments can define the following objects:
 
 ### Processors in Plugins
 
+::: warning
+File Extension-named Processors are deprecated and only work in eslintrc-style configuration files. Flat config files do not automatically apply processors; you need to explicitly set the `processor` property.
+
+**From ESLint v9.0.0+, File Extension-named Processors will be removed.**
+:::
+
 You can add processors to plugins by including the processor functions in the `processors` key. For more information on defining custom processors, refer to [Custom Processors](custom-processors).
 
 ```js