fix(warp): don't send task-complete while background tasks are still running

[neeilya]

Problem

on-stop.sh sends the task-complete payload on every Claude Code Stop event. But Stop fires whenever the main agent's turn ends, including:

1. the turn that launched background sub-agents (Agent tool) or background shells that are still running, and
2. every short re-invocation turn the harness runs when one of those tasks completes.

So a prompt that fans out to three sub-agents produces four "task complete" banners, three of them while work is still in progress, and Warp's session status flips to Complete and back to Working each time. Reported in #67 and #82.

Fix

Claude Code ≥ 2.1.145 includes a background_tasks array in Stop hook input listing in-flight sub-agents, shells, monitors, workflows and teammates (hooks reference). This is the official signal #82 asked for.

• New scripts/has-background-work.sh exposes has_background_work "$INPUT", true when any entry has status == "running".
• on-stop.sh and legacy/on-stop.sh exit silently when it is true. The Stop that fires after the last task completes has an empty array and sends the one real notification.
• Older Claude Code lacks the field, so behaviour there is unchanged. Only running counts, so an unfamiliar status fails open toward notifying rather than going silent.
• README updated to describe the new Stop behaviour.

No changes to the payload schema or protocol version.

Testing

• tests/test-hooks.sh: 66 passed, 0 failed. Adds unit tests for the helper (field absent, empty, running subagent, running shell, non-running entry, malformed input) and a routing test that on-stop.sh emits nothing with a running task and emits the stop terminalSequence once the array is empty.
• Captured real Stop payloads from Claude Code 2.1.263 with a background shell and a background sub-agent in flight (both status: "running") and ran them through both Stop scripts: suppressed with tasks running, notification sent with the array emptied.
• Live in Warp v0.2026.09.02.08.27.stable_01 with plugin 2.2.0 (unpatched): a prompt launching three background sub-agents produced four banners, matching the reproduction in Stop hook notifies on every sub-agent completion (<task-notification> re-invocations), spamming a banner per sub-agent #67.

Out of scope

session_crons (scheduled wake-ups from /loop, ScheduleWakeup, CronCreate) is left alone: a session idling between cron fires is arguably done with the current task, so it still notifies.

Closes #67
Closes #82

[neeilya]

@advait-m @liliwilson @vorporeal @zachbai