[checkpoint] Continue scicode_agent after verified sub-steps

Parent

Child of #3220 and #3024. No additional resource child.

State owner

responses_api_agents/scicode_agent/app.py owns sub-step cursor, generated scripts/responses, verification feedback, model/resource cookies, usage, and revision.

Adapter requirements

Use the shared whitebox participant and versioned boundary records. Persist output items, usage, cookies, last model-call identity, resource revisions, remaining budgets, and typed agent-specific state. Commit only after all effects of an operation are durable. On attempt N+1, skip reseeding and do not repeat completed model, tool, verifier, or judge work.

Acceptance criteria

• Restore after each verified sub-step continues with the next problem part without rerunning prior scripts or verification.
• Prepare/commit/process replacement/restore/resume succeeds at every supported boundary.
• Saved model responses, usage, cookies, and pending actions are applied exactly once.
• Checkpoint refusal retries without advancing history or the operation cursor.
• Resource revision mismatch, stale attempt, duplicate restore, and corrupt state fail closed.
• Completed-unacknowledged results cannot also be published as resumable work.

Start with responses_api_agents/scicode_agent/app.py and the parent issues #3220 and #3024. Trace the sub-step cursor, generated scripts and responses, verification feedback, cookies, usage, revisions, and checkpoint boundaries described in the issue. Done means every listed acceptance criterion holds, including exact-once resume behavior and fail-closed handling of invalid state.