Migrate `withRouter` from an integration to an e2e test (#67721)
There's apparently some interference with other tests when running the
`withRouter` integration test in the CI, which leads to [frequent test
failures](https://app.datadoghq.com/ci/test-runs?query=test_level%3Atest%20env%3Aci%20%40git.repository.id%3Agithub.com%2Fvercel%2Fnext.js%20%40test.service%3Anextjs%20%40test.suite%3A%2AwithRouter%2A%20%40test.status%3Afail&agg_m=count&agg_m_source=base&agg_t=count¤tTab=overview&eventStack=&fromUser=false&index=citest&start=1713009743249&end=1720785743249&paused=true).
In lieu of identifying the interference source, we can refactor the test
to an e2e test. This should also fix the flakiness.
closes
[NDX-64](https://linear.app/vercel/issue/NDX-64/investigate-flakiness-of-testintegrationwith-router)
closes #67706