Builds the manager around the consumer's sync function.
The sync to fire on each tick.
Sink for a rejected sync.
Auto-sync cadence; false or 0 disables it.
Clears the pending timeout on disposal, preventing leaked timers.
Cancels any pending auto-sync tick.
Schedules the next tick when an interval is armed; the sync runs fire-and-forget so a rejection is logged, never propagated.
Updates the cadence and reschedules from now.
New interval; false or 0 disables the timer.
Manages periodic auto-sync with a configurable interval. Drives the consuming clients' periodic registry refresh.