Applications in KDE can send notifications, which result in popups on the task bar:
Highly annoying this is. The culprit is that control-shift-A is the shortcut to enabling this behavior, as is shown via “Konsole -> View -> Monitor for Activity”:
It’s fortunate that this is easy to disable. Right click on “Monitor for Activity -> Configure Shortcut”, then click on “Ctrl+Shift+A”, which will then display “Input”. Click on the left arrow graphic:
That should result in it showing “None”, which means that there will no longer be a shortcut. You might want to go back to “Konsole > View” and make sure that “Monitor for Activity” is not checked.
I seem to do this every time I set up KDE, so perhaps this will help others.