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Issue Description

When installing @typescript-eslint/[email protected] and importing it into a TS file (which causes it to be type-checked), @typescript-eslint/eslint-plugin/index.d.ts throws the following two TypeScript errors (with the latest version of TypeScript, 5.1.6):

node_modules/@typescript-eslint/eslint-plugin/index.d.ts:1:31 - error TS2307: Cannot find module '@typescript-eslint/utils' or its corresponding type declarations.

1 import type { TSESLint } from '@typescript-eslint/utils';
                                ~~~~~~~~~~~~~~~~~~~~~~~~~~

node_modules/@typescript-eslint/eslint-plugin/index.d.ts:3:24 - error TS2307: Cannot find module './rules' or its corresponding type declarations.

3 import type rules from './rules';

Reproduction Repository Link

https://github.com/typescript-eslint/typescript-eslint/files/12035147/repro.zip

Repro Steps

1. download and extract repro.zip
2. npm i
3. npx tsc

Versions