When the user opens a different dashboard in the designer, it assigns a new report object — onAssignedReport lets you capture it.

In React.
import { Designer, Stimulsoft } from "stimulsoft-dashboards-js-react/designer";

function App() {
    var report = new Stimulsoft.Report.StiReport();
    report.loadFile("Dashboards/Dashboard.mrt");

    var options = new Stimulsoft.Designer.StiDesignerOptions();
    options.appearance.fullScreenMode = true;

    function onAssignedReport(args: Stimulsoft.Designer.AssignedReportArgs) {
        report = args.report;
    }

    return <Designer options={options} report={report} onAssignedReport={onAssignedReport} />;
}

How it works. The event fires whenever the designer swaps its dashboard, so your component always holds the current one.