Function run_dm_pump 

async fn run_dm_pump(
    host: Arc<dyn SlackHost>,
    client: Arc<dyn SlackApi>,
    workspace: String,
    interval: Duration,
    shutdown: Receiver<()>,
)

Sweep the DM class on its own task and its own clock, until shutdown fires. The first pass runs at once - a restart has a gap to catch up on - and every one after it waits the interval.