First I tried the button Recovery in the Updraft Settings. A window showed up that said it will download, then a progress bar appeared and a sign that db0 is downloaded. Then - nothing for about ten minutes.
Was it downloading it from some remote storage? Presumably something failed there - if you turn on debug mode (in the expert settings at the bottom of the 'Settings' tab), then it generates a log file in wp-content/updraft when downloading from remote storage, and then can be investigated.
However - another way to do it is to grab the file from remote storage manually (e.g. visit http://www.dropbox.com, or wherever), and place the file via FTP in wp-content/updraft; then click on the "Rescan local storage" link in UpdraftPlus, and it will then be able to proceed. Or, after getting it from the remote storage, upload it via the drag/drop uploader in UpdraftPlus - this uses chunked uploading to bypass any web hosting company upload limits.
Then I tried to import the file into the database via phpmyadmin and there was an import file limit of 20megs. That's when I thought maybe that's the problem with the first try, too.
No, that wouldn't be the problem with the other method - PHP has a maximum file upload limit, but that limit doesn't come into play in any of the normal ways of getting a backup set into UpdraftPlus. Obviously, there was something - but not that.