I tried to add a new action to the main toolbar using "Configure Toolbars" in "Settings". When applying the change, the toolbar disappeared completely, and the menu bar was incomplete as well, e.g. the "Settings" tab was missing.

I had the same problem when changing the icon for the KCalc tool (select /usr/share/icons/oxygen/16x16/apps/accessories-calculator.png). On re-entering KMM, the new icon was there, and so was the new action.

Is this behavior known? Can it be fixed?

Yes it is known: https://bugs.kde.org/show_bug.cgi?id=235937 and it could probably be fixed, but for now, we did not find someone with enough foo to do it.