When the toolbar is changed in the KDE version using "Settings/Configure Toolbars" the menus are broken, they only contain the non-standard actions. This does not only occur with Kid3 3.0 but also with earlier versions. The change of the toolbar lets KDE create a new ui file in ~/.kde/share/apps/kid3/kid3ui.rc, however all menu entries in this new ui file have a noMerge attribute, which makes that "the standard menu layout from ui_standards.rc won't be used" (according to kpartgui.dtd). This breaking change was introduced into the KDE libraries and seems to affect other applications too, see for instance https://bugs.kde.org/show_bug.cgi?id=306258.
A workaround is to delete ~/.kde/share/apps/kid3/kid3ui.rc. A solution is to include all actions in the ui file, not only the non-standard actions, see the associated patch.