Keep CLI harness sessions in progress while background work is pending

[warp-agent-staging]

Description

Third-party harness runs (Claude Code) reported SUCCEEDED on every assistant turn and IN_PROGRESS on the next one, because the warp plugin's Stop hook was mapped 1:1 to task success. Claude Code starts turns on its own whenever background work completes (run_in_background Bash, Monitor watches, subagents, session crons), so a run babysitting a build flapped between the two states on every wake — each SUCCEEDED fanning out to GitHub/Slack/Linear notifiers ("Warp has completed this task." per heartbeat), the lifecycle notifier, usage charging, and the idle-exit timer. The idle timer side also meant a run waiting on a long subagent could be /exited at --idle-on-complete while the subagent was still running.

Claude Code's Stop hook input includes background_tasks and session_crons, which exist precisely to distinguish "session is done" from "session is paused waiting for background work to wake it back up". The warp plugin (2.4.0, warpdotdev/claude-code-warp#92) now forwards both counts on the stop event. On the client, a Stop that carries pending work updates the session's context but leaves its status untouched: no StatusChanged is emitted, so LocalAgentTaskSyncModel reports nothing and the driver does not arm the idle timer, until a Stop with nothing pending arrives. finish-task, the /exit path, and the exit-time SUCCEEDED fallback in AgentDriver::flush_task_status_before_exit are unchanged.

MINIMUM_PLUGIN_VERSION for Claude moves to 2.4.0 per the plugin repo's versioning policy, so the driver updates older installs. The plugin PR must land first; until the marketplace serves 2.4.0, the (non-fatal) notification-plugin update step logs a failure on each run.

This replaces the earlier debounce approach on this branch, which is fully reverted.

Known tradeoff: a background task that never finishes (or whose completion notification Claude Code drops) now keeps the run IN_PROGRESS with no idle timer until the sandbox deadline, instead of exiting at idle-on-complete.

Linked Issue

Ad hoc intake; no tracked issue.

• The linked issue is labeled ready-to-spec or ready-to-implement. — No tracked issue.
• Where appropriate, screenshots or a short video of the implementation are included below. — Not applicable: no UI changes.

Testing

• cargo nextest run -p warp cli_agent_sessions — 180 passed. Two new tests: a stop with background_task_count: 1 leaves the session InProgress while still recording the response; a stop with zero counts still yields Success.

• cargo nextest run -p warp local_agent_task_sync_model plugin_manager — 135 passed (sync model is back to master).

• cargo clippy -p warp_core -p warp --all-targets --tests -- -D warnings — clean; ./script/format run last.

• Confirmed Claude Code 2.1.252 populates background_tasks for an in-flight background shell task (Stop Search history by more than just command #1) and reports it empty on the post-notification turn (Stop Real-time collaboration #2).

• End-to-end on the local Oz stack (script/oz-local, direct backend, this branch's bundle, local plugin checkout): a Claude run that starts sleep 60; echo finished in the background, replies, and is woken by the task-notification now produces exactly one agent_started and one oz_run_done (at the final turn), versus two pairs before this change.

• I have manually tested my changes locally with ./script/run

Agent Mode

• Warp Agent Mode - This PR was created via Warp's AI Agent Mode

CHANGELOG-BUG-FIX: Claude Code harness runs no longer report completion and re-open on every assistant turn while background tasks, subagents, or scheduled wakeups are still running; completion is reported once the session is actually idle, or immediately on finish-task.

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