[fix] Correct AppType generic prop handling

[ash2228]

Fixes [#44434] (#44434)

Problem

• AppType<P> incorrectly applied P to pageProps instead of root props
• Type checking didn't match runtime behavior

Solution

Modified AppType definition in utils.ts to:

export type AppType<P = {}> = NextComponentType<
  AppContextType,
  P & { pageProps?: any },
  AppPropsType<Router, P>
>

[ijjk]

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[ash2228]

This is my first contribution. I've:

• Fixed the AppType typing issue
• Added test coverage
• Verified the core functionality works locally

The CI failures appear unrelated to my changes. Could you:

1. Confirm if these are known environment issues?
2. Suggest how I can help resolve them?

[ash2228]

@ijjk Thanks for the review!

• Confirmed the type fix works locally
• Tests pass as shown in the reproduction
• Ready for CI approval when convenient

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[timneutkens]

Thanks for the PR. At this point we're not making changes to the Pages Router types in order to be fully backwards compatible with existing applications.