Keep the FO running across handoffs and status questions

[clkao]

Keep authorized workflow work moving across handoffs while respecting captain decision boundaries.

What changed

• Define continuation and stopping conditions.
• Keep Codex monitoring active after status answers.
• Make the Claude harness suffix defer to declared stops.

Evidence

• Previous combined-tip CI: Codex and Claude continuation/rejection scenarios passed. No causal improvement over the historical baseline is claimed.
• Restacked above Make state transitions durable #803 with unchanged owned patches; independent suffix review preserves strict graders.
• Reordered lower tip 6a575d7: normal/race passed every package except the existing cached-pre0 installed-host resolver failure; no race diagnostics. Live-tag compilation passed. Exact verification report.

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Closes #735