[Doc] Fix broken references in serve documentation

[peytondmurray]

Why are these changes needed?

This PR fixes broken links in Serve documentation in preparation for turning on Sphinx's nitpicky mode.

Related issue number

Partially addresses #39658.

Note: The version increase of autodoc_pydantic is needed to support @root_validator-decorated pydantic models, and is made possible by #40451.

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 :(