[Serve] Deflake and re-enable client serve test

[architkulkarni]

Why are these changes needed?

Reverts #14733.

Ideally we would run this test, say, 10 times in a loop in the test to really ensure it's no longer flaky, but disconnecting and reconnecting the Ray Client still doesn't work with Serve (even with a non-detached Serve instance) so this isn't possible at the moment.

Related issue number

Checks

• I've run scripts/format.sh to lint the changes in this PR.
• I've included any doc changes needed for https://docs.ray.io/en/master/.
• I've made sure the tests are passing. Note that there might be a few flaky tests, see the recent failures at https://flakey-tests.ray.io/
• Testing Strategy
  • Unit tests
  • Release tests
  • This PR is not tested :(

[edoakes]

Looks good. 2/2 passed on the PR build and it was deflaked upstream, so we should be ok here.