In my case, I wanted typescript, but didn't get it installed.
This question still helped me figure out my problem which is described below.
I was watching a YouTube video, React Typescript Tutorial that explained how to get started with typescript and react, and the video said to run:
npx create-react-app cra-ts --typescript
This didn't work (but I didn't know it). As soon as I created a hello.ts file, I got the error the OP describes.
Error: Failed to load parser '@typescript-eslint/parser' declared in 'package.json » eslint-config-react-app#overrides[0]': Cannot find module 'typescript'
The fix was to use the command:
npx create-react-app myappts --template typescript
This used [email protected] and [email protected].
ProTip: If your newly created React App doesn't have a file named App.tsx, then you haven't actually created it correctly.