I deleted one of the sync stores, and things seem to be all right, having done that. I have no idea why it became duplicated in the first place.
I mentioned the 4.0.2 release because the forum query which seemed most similar to this was someone complaining that “the iCloudKit sync location is showing twice and WebDAV is showing three times”, to which @eboehnischreplied “This is a known bug and fixed in version 4.0.2”.
As to the share sheet, there are iOS apps in which it doesn’t appear to work. Say I select a document in Apple’s Notes app, then tap the “arrow pointing up from the box” icon at top, and choose the DEVONthink icon. Nothing happens. Someone wrote a shortcut which overcomes this, and this works well in the share sheet. (The DEVONthink icon method does however work in Apple’s Photos and Safari apps, I notice.)