Function pause 

pub async fn pause(
    context: &PauseWorkflowContext<'_>,
    id: &WorkflowId,
    run: &RunId,
    reason: Option<String>,
    operator: Option<String>,
) -> Result<WorkflowHandle, EngineError>

Pauses a live, Running run: appends WorkflowPaused through the resident handle’s own recorder (single-writer, cancel precedent) and inserts the run into the shared dispatch-hold set. The resident process is left alive.

Errors

Returns EngineError::WorkflowNotFound when no history / no resident handle exists for (id, run), and EngineError::InvalidState — naming the actual status — when the run is not Running (e.g. Completed, already Paused). A rejection appends nothing to history.