KEP-3562: [OptimizationJob] Implement Shared Initializer for state restoration

### What you would like to be added?

Context:
In Phase 2 of [KEP-3562](https://github.com/kubeflow/trainer/pull/3565), OptimizationJob aims to support warm-starting experiments and restoring state from previous runs.

Problem:
Currently, starting a new optimization experiment requires re-evaluating all baseline parameters, even if similar historical jobs exist.

Future Goals:

- Introduce a Shared Initializer component to load pre-existing trial history or pre-trained weights.
- Allow OptimizationJob to restore state directly into the Optuna suggestion container upon startup.

We have an existing KEP for the Shared Initializer : https://github.com/kubeflow/trainer/pull/3311

Relates to KEP-3562 Master Tracking [Issue](https://github.com/kubeflow/trainer/issues/3562).

### Why is this needed?

A Shared Initializer enables warm-starting complex tuning jobs, saving significant time and compute cost when iteratively tuning large models.

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