KDE-Forum.org

I'm not a SuSE user, but here is a guess: do the panel options show any option (under the section K Menu)?

I would appreciate it if a real SuSE user would jump in and tell the answer right away.

Perhaps, this search bar isn't configurable. It's the thing, that SuSE call "menu extension".
To remove all such things, I just build KDE from sources.

I guess you may try following:
Go to /etc/sysconfig/windowmanager and set these variables:
INSTALL_DESKTOP_EXTENSIONS="no"
CREATE_XDG_MENUS="false"
KDE_BUILD_GLOBAL_SYCOCA="no"

then run "kbuildsycoca" to rebuild KDE menu cache. This will turn back original KDE menus, instead of SuSE extensions.

But. I'm not sure at all, that it will work and this can harm your system. In any case, backup your $HOME/.kde folder before proceeding.