[CI] Deflake doctest CI

[bveeramani]

Why are these changes needed?

Doctests are flaky for three reasons:

• tips-for-first-time.rst is failing because Ray is re-initialized in some examples. This wasn't an issue before because most of the examples were skipped. However, after [Docs] Fix docstring examples with mocked outputs #35928, all of the examples are run. To fix this issue, I've added cleanup code that shutsdown Ray between examples.
• async_api.rst is flaky because print calls from a previous example manifests in subsequent examples. To avoid flakiness, I've added a short sleep after the example that prints asynchronously.
• loading-data.rst fails for one of two errors reasons: Either the Python frontend falsely determines that Ray is initialized, so the app complains The core worker process is not initialized yet or already shutdown.; or, the Python frontend thinks Ray isn't initialized and tries to re-init, but the back is actually already initialized. In either case, it seems like the backend and frontend go out of sync. I wasn't able to figure out the underlying issue, so I'm disabling the test for now.

Related issue number

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 :(