[Serve] [doc] Improve runtime env doc

[architkulkarni]

Closes #18781.

• Update code snippet to use dynamically installed pip packages instead of preinstalled conda environments
• Test snippet in CI
• Add best practice to doc: for packages that build from source, precompile rather than putting in runtime env

https://ray--18782.org.readthedocs.build/en/18782/serve/core-apis.html#dependency-management

Why are these changes needed?

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 :(