updated api-routes-apollo-server-and-client example to utilize app router.

[PapatMayuri]

This PR updates the api-routes-apollo-server-and-clientexample for using the App Router.
Here are the changes that have been made:

• I renamed the pages folder and moved it to the app folder.
• Added the layout.tsx file as part of the App Router.
• Moved component folder to app folder.
• Moved api folder to app folder.
• Added apollo folder to lib folder
• Updated the package.json file.

CC: @samcx

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[samcx]

@PapatMayuri Please make sure to test the example before pushing up a PR and having it ready for a review. Unfortunately, this one has a multitude of issues.

You may have update the example to be something like this → https://github.com/apollographql/apollo-client-nextjs/tree/main/examples/app-dir-experiments.

[PapatMayuri]

Sure @samcx, Thanks for the feedback. I'll make sure to test the example thoroughly before submitting a PR and will follow the approach outlined in the (https://github.com/apollographql/apollo-client-nextjs/tree/main/examples/app-dir-experiments). I'll also address any issues that arise during testing to ensure everything works smoothly before submitting for review.

[PapatMayuri]

Hi @samcx I have updated the example please check & let me know if there are any changes needs to be done.

[samcx]

@PapatMayuri This example is still not working. Did you make sure to run the example?

[PapatMayuri]

Yes @samcx I checked the example it is working. Give me some time I will recheck and update you.

[vercel]

Notifying the following users due to files changed in this PR based on this repo's notify modifiers:

@timneutkens, @ijjk, @shuding, @huozhi:

packages/next/src/server/config.ts