Exporting 'data with current layout' doesn't work on the Report Server (September 2022) for reports created in the Power BI Desktop (September 2021).
Yes, I created many reports in Power BI Desktop (September 2021) optimized for Power BI Report Server. In each of the reports published on Report Server (September 2022), export option 'data with current layout' on the Server web page is always greyed out, even for table or matrix visual. I didn't try do this in Power BI Desktop (September 2022), because I don't have it yet.