Thanks for coming back to me.
Yes to backup, I have had the extension for a few years on our site. We backup before upgrading anything no matter how small.
I upgraded to 3.9.9 and then upgraded JDownloads. After that we upgraded to 3.9.10 but a little while after.
I can't say whether the extension failed at 3.9.9 however, things have moved on since reporting this.
With the Joomla logging set to Default everything works fine, when at maximum I get the error. Additionally I get the "Trying to get property 'id' of non-object in" everywhere on the site when the logging is higher so I think the issue is not with JDownloads.
I will continue to play but right now everything is fine with the logging set to default.