Rewrite optimize() to use ax.api.client.Client, remove OptimizationLoop (#5143)

Summary:
Pull Request resolved: #5143

**Goal:** Eliminate legacy code that keeps other legacy code alive. Even though managed loop is deprecated, it has internal use cases. It seemed easier to migrate it then to try to clean up every single use case.

The `OptimizationLoop` class in `managed_loop.py` was a legacy managed optimization loop that used `choose_generation_strategy_legacy`. This diff:
- Rewrites the deprecated `optimize()` function to use the modern `ax.api.client.Client` API
- Removes the `OptimizationLoop` class entirely (no external callers)
- Splits `managed_loop` into its own BUCK target with minimal dependencies
- Updates tests and LLM rules to reflect the changes

The `optimize()` function signature and return type are preserved for backward compatibility with existing callers.

Reviewed By: esantorella

Differential Revision: D99497269

fbshipit-source-id: dc27a30e0637f62baa05714e4ab4ef120295abea

Author: saitcakmak

ax/service/__init__.py

@@ -5,8 +5,3 @@
 # LICENSE file in the root directory of this source tree.
 
 # pyre-strict
-
-from ax.service.managed_loop import OptimizationLoop, optimize
-
-
-__all__ = ["OptimizationLoop", "optimize"]