I don't distinguish between KDE/Plasma apps living in the System Tray, and Plasma Widgets A.K.A. Plasmoids. I never see my desktop, as I run most applications full screen, so I have no widgets there. The widgets I use are in the panel, so for me there is no difference.
One of the "simple" apps I use all the on the Plasma desktop is Klipper, the Plasma™ clipboard cut & paste utility.
Klipper is a clipboard manager for the KDE interface. It allows users of Unix-like operating systems running the KDE desktop environment to access a history of X Selections, any item of which can be reselected for pasting. It can also be used to react automatically if a certain text is selected (e.g. opening an URL in a browser). Wikipedia
It's been around for ever (as long as forever is in the software world) and has hardly changed it's look and features over the years.
I tried to develop a similar app for Sailfish OS, but apparently it is not as easy under Wayland, which the KDE people also recognizes.
KNotes, the computer equivalent of sticky notes, is an old acquaintance in KDE, now Plasma.