Where is Apple Health data "Exported"? After chasing the "Export Health Data" option in Apple Health, and waiting a long time without feedback or any notification the initial dialing that is presented (see below) disappears, and nothing appears to happen. This is worse than (already bad) past experiences I've had with this feature, and seems to produce no result at all.

Where should I look for the (alleged) export of Apple Health data?
As @fsb commented, you should get an options pane where you select where you want to store the export.zip file created by the Health App.  You can save it to one of many options including Airdrop, 'Files', Dropbox, Notes, or other options. If you didn't get the pane to select where to store your data, then maybe it wasn't finished preparing your data. On my iPhone 6 running iOS 12.4.1, the selection pane appears automatically after preparing your data.