fix(linter): install @eslint/eslintrc package as necessary (#29933)

When flat compat is necessary, we don't ensure that `@eslint/eslintrc`
is installed, even though we import it. Depending on the package manager
and hoisting, it may still work, but as we see with pnpm v10, it is not
working without an explicit dependency in `package.json`.

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## Current Behavior
Some app generators are broken is we use eslint compat.

## Expected Behavior
App generators should work.

## Related Issue(s)
<!-- Please link the issue being fixed so it gets closed when this is
merged. -->

Fixes #29845

Author: jaysoo

packages/eslint/src/generators/utils/eslint-file.spec.ts

@@ -120,6 +120,45 @@ describe('@nx/eslint:lint-file', () => {
       ]);
     });
 
+    it('should install necessary dependencies', () => {
+      // mock eslint version
+      jest.spyOn(devkitInternals, 'readModulePackageJson').mockReturnValue({
+        packageJson: { name: 'eslint', version: '9.0.0' },
+        path: '',
+      });
+      tree.write('eslint.config.cjs', 'module.exports = {};');
+      tree.write(
+        'apps/demo/eslint.config.cjs',
+        `const baseConfig = require("../../eslint.config.cjs");
+
+module.exports = [
+  ...baseConfig,
+  {
+    files: [
+      "**/*.ts",
+      "**/*.tsx",
+      "**/*.js",
+      "**/*.jsx"
+    ],
+    rules: {}
+  },
+];`
+      );
+
+      addExtendsToLintConfig(tree, 'apps/demo', {
+        name: 'plugin:playwright/recommend',
+        needCompatFixup: true,
+      });
+
+      expect(readJson(tree, 'package.json').devDependencies)
+        .toMatchInlineSnapshot(`
+        {
+          "@eslint/compat": "^1.1.1",
+          "@eslint/eslintrc": "^2.1.1",
+        }
+      `);
+    });
+
     it('should add extends to flat config', () => {
       tree.write('eslint.config.cjs', 'module.exports = {};');
       tree.write(

packages/eslint/src/generators/utils/eslint-file.ts

@@ -20,7 +20,11 @@ import {
   useFlatConfig,
 } from '../../utils/flat-config';
 import { getInstalledEslintVersion } from '../../utils/version-utils';
-import { eslint9__eslintVersion, eslintCompat } from '../../utils/versions';
+import {
+  eslint9__eslintVersion,
+  eslintCompat,
+  eslintrcVersion,
+} from '../../utils/versions';
 import {
   addBlockToFlatConfigExport,
   addFlatCompatToFlatConfig,
@@ -493,13 +497,19 @@ export function addExtendsToLintConfig(
       return addDependenciesToPackageJson(
         tree,
         {},
-        { '@eslint/compat': eslintCompat },
+        { '@eslint/compat': eslintCompat, '@eslint/eslintrc': eslintrcVersion },
         undefined,
         true
       );
     }
 
-    return () => {};
+    return addDependenciesToPackageJson(
+      tree,
+      {},
+      { '@eslint/eslintrc': eslintrcVersion },
+      undefined,
+      true
+    );
   } else {
     const plugins = (Array.isArray(plugin) ? plugin : [plugin]).map((p) =>
       typeof p === 'string' ? p : p.name