[Feature] Add background subagent lifecycle v1.1

[Astro-Han]

What task are you trying to do?

We want PawWork to add the background half of the agent lifecycle now that #283 v1 has shipped through PR #287. The current v1 is intentionally foreground-only: agent blocks until terminal, lifecycle state is persisted through SubagentRun, and the model can inspect owned runs through agent_list and agent_output. This issue scopes the next step: background subagents that can keep running after the parent turn returns, then notify and resume safely when they finish.

What happens today?

PR #287 implemented the foreground lifecycle foundation: explicit running, completed, completed_empty, failed, and canceled_by_user states; a per-parent concurrency cap; agent_list; agent_output; resume validation; and parent-owned lifecycle persistence. The deferred pieces from #283 are still not present: run_in_background, parent-session completion notifications, safe auto-resume, agent_stop, blocking output reads, and restart cleanup for stranded running rows.

What would a good result look like?

agent supports run_in_background?: boolean while preserving the existing foreground default. A background subagent returns quickly with a clear running status and enough identity for later inspection. Terminal background states inject a parent-session notification and trigger safe auto-resume only when the parent can continue without surprising the user. The model can inspect background progress through the existing agent_list / agent_output tools. Any new stop or blocking-read tool surface must be justified by the background lifecycle, not added speculatively.

Scope

• Add run_in_background?: boolean to agent, default false.
• Reuse the existing SubagentRun lifecycle vocabulary and parent-owned state.
• Preserve agent as the spawn entry point; keep agent_list and agent_output as narrow lifecycle query tools.
• Add parent-session terminal notification for background completion, failure, cancellation, and empty output.
• Define safe auto-resume rules so the parent can react to background completion without continuing blindly.
• Decide whether agent_output needs block?: boolean / timeout_ms?: number once background reads exist.
• Add agent_stop only if background execution gives the model a real re-entrant point where stopping a child is useful.
• Add an abandoned or equivalent startup sweep for persisted running rows left behind by host restart.

Non-goals

• Do not replace the current three-tool model with agent({ action: ... }). The current shape matches Claude Code-style best practice: spawn is one tool, lifecycle inspection is handled by narrow companion tools.
• Do not add a new task panel, global background-task UI, or full task system.
• Do not add nested subagents.
• Do not add automatic backgrounding heuristics in this issue.
• Do not mix in worktree/session execution-context changes; those belong to [Feature] Agent session lacks worktree isolation — worktree is a project concept, not a session context #278.
• Do not add cross-parent session management.
• Do not implement full transcript pagination.

Acceptance criteria

• agent({ run_in_background: true }) starts a background subagent and returns a clear running result without blocking the parent until terminal.
• Foreground agent behavior remains the default and stays backward-compatible with PR feat(agent): subagent lifecycle v1 (foreground-only) #287.
• Background and foreground runs share the same persisted lifecycle states and authorization model.
• agent_list includes running background runs and unread terminal background runs under the existing all_active behavior.
• agent_output can inspect running background runs without consuming them, and consumes only terminal rows on first read.
• Background terminal states notify the parent session with enough structured context for the model to continue safely.
• Safe auto-resume behavior is specified and tested, including cases where the parent should not resume.
• User cancellation and model/tool failure finalize background runs as explicit lifecycle states, never empty output.
• Host restart does not leave old persisted running rows looking live forever; the startup sweep marks them with a clear terminal or abandoned state.
• If agent_stop is added, it can stop only subagents owned by the current parent session and returns the same lifecycle vocabulary.
• Tests cover foreground compatibility, background launch, notification, auto-resume gating, output reads, cancellation, failure, restart cleanup, and authorization.

References

• [Feature] Make agent tool lifecycle explicit, visible, and schedulable #283: original agent lifecycle design and v1 foreground scope.
• PR feat(agent): subagent lifecycle v1 (foreground-only) #287: foreground-only lifecycle implementation.
• [Feature] Agent session lacks worktree isolation — worktree is a project concept, not a session context #278: separate worktree/session execution-context design, intentionally out of scope here.
• Claude Code reference direction: Agent is the spawn tool, while task/output/stop/message surfaces remain separate narrow tools rather than one Agent(action=...) envelope.