Support cache-preserving reasoning changes with configuration_update input items

Problem statement / motivation

The Responses API can change reasoning effort between responses by appending a configuration_update item while keeping request-level reasoning.effort unchanged. Agentic API has no typed variant for this item. It becomes Unknown, loses its payload, and is excluded from persisted input history.

Proposed solution

Add typed configuration-update items and preserve their position through input handling, storage, rehydration, and upstream serialization. Track the effective effort separately from the initial request-level setting. Gate execution on upstream capability; an unsupported backend must reject the operation before inference instead of silently changing semantics.

Acceptance criteria

• HTTP and WebSocket requests accept supported updates, including manually replayed histories and previous_response_id continuation.
• An update applies to subsequent responses until superseded; branching histories preserve their own effective settings.
• The original request-level effort and preceding item history remain unchanged; public response metadata follows the documented contract.
• Reject adjacent updates and unsupported mode combinations. The current reference supports standard single-agent mode, excludes automatic compaction/truncation, and rejects updates at the standalone compact endpoint.
• Explicit compaction_trigger behavior is covered, including a fresh update after compaction.
• Tests cover malformed updates, unsupported effort, multiple turns, stored/transient state, and unsupported-backend errors. Cache-prefix assertions verify serialized input stability, not an assumed cache hit.

Additional context

Related: #314 (request capabilities), #298 (multi-agent compatibility boundaries). This issue changes API state and forwarding; it does not move prompt rendering or cache execution into the gateway.

Source: change reasoning mid-conversation.

Reviewed at cdac36f: implementation. Documentation checked September 18, 2026; pin the implementation-time API/model version when recording conformance.

Start with crates/agentic-server-core/src/types/io/input.rs at the reviewed implementation, then trace input handling, storage, rehydration, and upstream serialization from there. Use the acceptance criteria to define done: supported updates preserve history and effective settings across HTTP, WebSocket, continuation, and compaction cases, while malformed or unsupported operations are rejected and the listed state, forwarding, and cache-prefix tests pass.