Refactor playground to be more useful

[amannn]

Currently, https://github.com/amannn/next-intl/tree/main/examples/example-app-router-playground is used for e2e testing.

That's absolutely fine, but I think if we'd refactor it to something like https://app-router.vercel.app it could also be helpful to document more advanced use cases.

Therefore, I'd propose to refactor the playground example to:

1. Look nicer and be approachable to users
2. Keep all existing tests
3. Group tests logically into different sections of the app (i.e. no home page that demonstrates all kinds of wild patterns)

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Related to this, https://next-intl-example-app-router.vercel.app is also a bit random in what it demonstrates. It's a basic test for i18n routing, it might make sense to clarify which patterns to demonstrate on this example and potentially include a few more features like date formatting. This is TBD.