I've honestly about given up trying to account for all the tweaking, injecting, and general tomfoolery that Plasma/KDE does with their platform Qt5 (via themes and plugins and such). But some things to try might be:
1) From your screenshots, I see the icons are disappearing in the Book Browser Treeview after dragging files. We've very, very, very recently pushed a fix related to disappearing icons and other file-reordering issues. You could try cloning the Sigil github repo and building the very latest master branch.
2) Install my stand-alone version of 0.9.9 (sticky thread above). It doesn't use all the whistles and bells that the platform plugin tries to add to Qt apps on KDE/Plasma. In fact, it doesn't use the platform's Qt5
at all.
3) Turn off the single-click-to-open "feature" in the system mouse settings. Single-click-to-open plays havoc with file selection in Sigil's Book View in general.
3) Launch Sigil with the command:
Code:
ssh -X localhost sigil
to avoid as much interaction with KDE as possible. If Sigil functions properly that way, the KDE Qt platform plugin is likely the issue.