I suppose your image from issue #298 could serve as an illustration here:
I think it depends on the compositor more than mousepad, for example I get two different behaviors with labwc (no icon) and wayfire (mousepad icon) by default.
It may also depend on whether or not CSDs are enabled in mousepad preferences (window tab, first option, mousepad must be restarted for this to take effect).
No, any application can choose to adopt client-side decorations (CSD), but maybe kwin forces server-side decorations (SSD), I don't know (no time to test kwin right now, sorry). Anyway, you can always try enabling CSD in mousepad as said above, if you haven't already.
For now that work-around works, but it's not ideal.
I'm not sure how to improve it, but having multiple different applications use the same icon is a problem regardless.