[Serve] Fix and unblock Serve flaky tests

[GeneDer]

Why are these changes needed?

Re: #42682 Startlette and fastapi issue have been fixed. Unblock Serve flaky tests.

Related issue number

Closes

• [serve] Re-promote flaky serve tests #42418
• [CI] linux:https://python/ray/serve/tests:test_api is failing/flaky on master. #42416
• [CI] linux:https://python/ray/serve/tests:test_model_composition is failing/flaky on master. #42415

Checks

• I've signed off every commit(by using the -s flag, i.e., git commit -s) in this PR.
• 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 added any new APIs to the API Reference. For example, if I added a
    method in Tune, I've added it in doc/source/tune/api/ under the
    corresponding .rst file.
• 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 :(

[GeneDer]

Also ran postmerge and seeing all serve tests passing https://buildkite.com/ray-project/postmerge/builds/2735#_

[edoakes]

Thx!