[eslint-plugin] ignore *.api.md files from linting (#31180)

### Packages impacted by this PR
`@eslint-plugin-azure-sdk`

common/tools/eslint-plugin-azure-sdk/src/configs/markdown-customized.ts

@@ -7,6 +7,7 @@ import typescriptEslint from "typescript-eslint";
 const markdownConfigs: FlatConfig.ConfigArray = [
   {
     files: ["**/*.md"],
+    ignores: ["**/*.api.md"],
     processor: "markdown/markdown",
   },
   {