I see this crash as well (MacOS 12.3.1, Designer 1.10.5). It seems to happen every time when in Export Persona, I change the name of the "Slice" that I want to export. After doing that, and clicking "Export Slice" I get the File save dialog, just as Michael posted, and the spinning cursor. The only option seems to be to force quit.
This is to save to the file to the desktop on my local disk--so it seems to have nothing to do with Cloud storage.
Reopening Designer, and NOT changing the name of the Slice (from Artboard1), the export works just fine. Changing the name of the slice, saving the file, quitting and restarting Designer, then the export works just fine.