fix(subagents): keep print-host parents from settling without wait

[tt-a1i]

Summary

• --print / --mode json cannot re-invoke the parent after agent_settled. Stock spawn text still tells the model it may end the turn; required child results are lost (E high-fast 3/10 print-settle failures).
• Non-TUI hosts now get spawn text that requires subagent_wait, plus a bounded followUp + triggerTurn barrier if the parent settles while direct children are running. Interactive TUI guidance is unchanged.
• Same E task+acceptor on cursor-grok-4.6-high-fast: 7/10 before (v0.8.1 stock) → 10/10 after. Isolated bun run check and bun run test pass. Closes nothing; tracks bug(subagents): --print/--json parent can settle while required children are still running [under investigation] #512. Do not merge from this reliability session unless a maintainer asks.

Test plan

• tests/extensions/subagents/print-host.test.ts and prompt contract
• bun run check && bun run test in isolated v0.8.1 worktree
• Real-model E high-fast n=10 after on the same acceptor
• Reviewer: confirm TUI fire-and-forget still says “end your turn”
• Reviewer: confirm print/json spawn result does not

[tt-a1i]

Self-review at exact head a10103d. I cannot formally request changes on a PR authored by this account, but the following are merge-blocking.

Standards

[P1] Print-host completion is still prompt-enforced rather than runtime-enforced. The agent_settled handler injects at most two “MUST call subagent_wait” follow-ups and then allows settlement while children may still run. The 10/10 experiment validates that the improved spawn wording influences this model; it does not establish a fail-closed lifecycle barrier.

[P1] runningDirectIds duplicates manager lifecycle state and misses valid transitions. A fast child can settle before the ID is added after spawn, leaving a stale running ID; a settled child restarted through subagent_send is never re-added. Please derive this state from the manager rather than maintaining a parallel Set.

Spec

[P1] Restarted direct children receive neither print-host wait guidance nor barrier tracking, so their required result can still be lost when the parent exits.

[P1] The fallback calls fire-and-forget pi.sendMessage() from agent_settled. Pi print mode can finish the original prompt and dispose before that nested turn completes; current tests assert pure helpers and the experiment runs all obeyed the earlier spawn guidance, so the fallback path has no end-to-end evidence.

[P2] The barrier counter is Session-global and never resets per spawn/batch, and RPC is included without protocol-level validation. The draft research records are also indexed under “Validated investigations.”