Okay, if a reset doesn’t work, try to send us a crash report via Settings: Privacy: Analytics: Analytics Data. There will hopefully be some entries for Scrivener in here, and when viewing the raw data for one, you’ll find a “share” button in the top right corner. Send that in to our support address so we can take a look at it.
In the meanwhile, please note the section in the Mac user manual under §14.2.1, Basic Usage, on page 358. Dropbox is only one way of getting data on and off the device, and so there are alternatives until this can be sorted out. (Note iOS 13 broke AirDrop support, so that option isn’t available at the moment.)
You can also of course use iTunes to roll your device back to the stable OS and wait for early bugs to be sorted out.