The thing with this tool is that you do not need to provide a source for elevation values, the tools uses an online service to get elevation values. That being said, you need to be online for it to work. I guess you might also need to have paid for maintenance for you ArcGIS Pro license to be able to access the elevations service that the tool uses. Here is the documentation for the tool in ArcGIS Pro 2.8: Summarize Elevation (Ready To Use)—ArcGIS Pro | Documentation. I cannot see why it should not work. Do you get any kind of error message when the tool fails? Anyway, I would recommend you to update to a newer version of Pro if possible.
A second way of achieving this is to download data from Terrain layer in Living Atlas and then use Add Surface Information. Below an image of how you can export a raster from the terrain layer once you have it opened in Pro and right-clicked it in the contents layer.
If this does not either work, I would recommend you to download data from Ordnance Survey and then use the Add Surface Information tool. I am not familiar with their products but this one seems to be free of charge: OS Terrain 50 | Data Products | Ordnance Survey