Turns v2 mode:background into a durable, in-API background execution service behind a BackgroundExecutionService facade. Adds the store layer (result/error columns, job_events durable milestone log, execution_signals control, heartbeat/lease, 3 migrations), the default backend (bounded executor, runner, in-memory live bus, liveness-aware single-flight orphan sweep), the v2 endpoint rewiring, and the real-instance test harness. Needs no new infra; works on the SQLite single-process install. The redis-scaled worker backend is stacked on top in a follow-up PR.