Add `llm-d` coordinator integration: hydrate and persist endpoints

[Mohammad-nassar10]

Problem statement / motivation

Let llm-d use agentic-api for Responses state without routing model traffic through the gateway. A stateful turn is exposed as two separately callable steps: hydrate before inference, persist after, so the caller makes the model
call itself.

This approach represents a separation of concerns between agentic-api which is responsible for all state management, hydration, etc., and llm-d coordinator, which is responsible for the AI request and response pipelines.

Proposed solution

• hydrate: resolve previous_response_id and return the upstream request with history inlined and continuation and storage fields removed, plus an opaque context for the turn.
• persist: take that context and the model's response, store the turn, and return the response envelope.

Both compose the functions the in-process executor already uses, so rehydration and persistence have one
implementation rather than two.

The endpoints are served by a separate crate and binary agentic-llm-d that depends on agentic-server-core and not on the gateway. It serves /internal/hydrate, /internal/persist, /health and /ready.

Alternatives considered

No response

Additional context

No response