In the good old Opera versions <= 12 it was possible with the described entry. And just after "dragging" an image some pixels it was opened in a new tab.
But dragging it onto the tab bar is a good workaround 😉
did you try resetting all flags?
opera://flags/
My bookmarks were gone because of tree-in-bookmarks flag, but Opera 27 still doesn't have that flag (I think)
maybe some other flag is messing with your bookmarks
Probably the installation options: all users, current user or standalone. Based on the location of the profile folder, standalone doesn't seem to be the case.
Do you have admin rights? Any program that may be clearing the files?