IDLE-DEFER should re-arm IsProcessing when background tasks are active

[PureWeen]

Problem

When SessionIdleEvent arrives with active background tasks but IsProcessing is already false (cleared by a prior watchdog timeout, EVT-REARM cycle, or permission recovery), the IDLE-DEFER path is a no-op — it flushes text but doesn't re-arm processing. The background tasks (sub-agents, shells) continue running but PolyPilot thinks the turn is done.

Observed

19:32:19 [IDLE-DEFER] 'PP- IC Things-worker-1' session.idle received with active background tasks 
  — deferring completion (IsProcessing=False, response=0+0 chars)

IsProcessing=False means the response was already finalized (truncated). The orchestrator collects a short/empty response and reports the worker as failed.

Expected

When IDLE-DEFER detects IsProcessing=false AND background tasks are active, it should re-arm IsProcessing=true (similar to EVT-REARM) so the session stays alive until the background tasks complete and a final idle (without background tasks) arrives.

Considerations

• Must follow INV-2 (UI thread for mutations)
• Must restart the watchdog (INV-9)
• Should log [IDLE-DEFER-REARM] for diagnostics
• The existing EVT-REARM path handles a similar case (TurnStart with IsProcessing=false) — the IDLE-DEFER re-arm would be analogous

Related

• PR Fix premature idle: check BackgroundTasks before completing #399: Added IDLE-DEFER (BackgroundTasks check)
• INV-18 in processing-state-safety SKILL.md