Group control and construction, target lifecycle, target-set transactions,
send pacing and commitment, and bounded timeout processing into private
children of the existing task owner. Keep durable status, outcome history,
top-level polling, sealing, and abandonment in task.rs.
Preserve phase-owned resources, stop/update synchronization, publication
ordering, pacing, and timeout fairness. Move the existing private gate and
timeout tests with their implementation without adding coverage or hooks.