[serve] Introduce context.py and client.py

[shrekris-anyscale]

Why are these changes needed?

Serve stores context state, including the _INTERNAL_REPLICA_CONTEXT and the _global_client in api.py. However, these data structures are referenced throughout the codebase, causing circular dependencies. This change introduces two new files:

• context.py
  • Intended to expose process-wide state to internal Serve code as well as api.py
  • Stores the _INTERNAL_REPLICA_CONTEXT and the _global_client global variables
• client.py
  • Stores the definition for the Serve Client object, now called the ServeControllerClient

Related issue number

N/A

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
  • This change relies on existing tests only.

[edoakes]

LGTM assuming all the copy-pasted logic is unmodified

[edoakes]

Test failure: https://buildkite.com/ray-project/ray-builders-pr/builds/29969#50c8e3a5-ea18-41c5-b6ac-2898a2b14dfb/6-7378