So I had some time to do some further testing into this issue and I made some "progress".
On my desktop, who has the correctly displayed light icons for the dark plasma theme: if I straight up remove ~/.cache (rename it to ~/cache.bak) and reboot, several icons become black (update, gajim and steam). Meaning that somewhere in that cache (but not ~/.share/icon-cache.kcache, since I tried that already), the correct display of icons is located.
I'll try to pinpoint it further and report back if I find anything.