fix: correct AppType props type usage

[snmsoodan]

Fix AppType generic being applied to pageProps instead of props

Closes #42846

Summary

The generic parameter P on AppType<P> was being applied to the pageProps
property of the App component's props instead of to the top-level props.

For example, with:

type MyInitialProps = { foo: string }

const MyApp: AppType<MyInitialProps> = ({ Component, pageProps, foo }) => {
  // ...
}

TypeScript reported Property 'foo' does not exist on type 'AppPropsType<any, MyInitialProps>'
for props.foo (even though foo exists at runtime), while props.pageProps.foo
was incorrectly allowed (even though foo is not on pageProps at runtime).

This happened because AppType<P> was defined as:

export type AppType<P = {}> = NextComponentType<
  AppContextType,
  P,
  AppPropsType<any, P> // <-- P was used as the pageProps type
>

Change

Apply the generic P to the top-level props instead of to pageProps:

export type AppType<P = {}> = NextComponentType<
  AppContextType,
  P,
  AppPropsType<any, any> & P // <-- P is merged into the App's props
>

Now props.foo is correctly typed (from P), and pageProps remains a separate
property of props (typed any, since AppType cannot know the page's props).
If a user wants to type pageProps, they can include it in P.

Why this is correct

• App.getInitialProps populates the top-level props of the App component,
  not pageProps (only a page's getStaticProps/getServerSideProps/
  getInitialProps populate pageProps).
• pageProps should remain a property of props, per maintainer guidance.
• The change is scoped to AppType only, so AppProps<P> (the type most _app
  files use, where P is the pageProps type) is completely unaffected.

Verification

• Reproduced the reported error with the current definition.
• Confirmed the fixed definition compiles with foo on props and pageProps
  as a separate property.
• Confirmed the existing test/e2e/typescript/pages/_app.tsx usage
  (AppType<{ foo: string }> with { Component, pageProps }) still compiles.
• Confirmed AppProps<P> behavior is unchanged.

Files changed

• packages/next/src/shared/lib/utils.ts

---

Note: This PR was prepared with the assistance of GitHub Copilot (an AI
coding agent). The change and verification were produced autonomously and
reviewed before submission.