The setting to change icon sizes, located in Settings > Appearance > Icons > Advanced, seems to have been unusable for years, as you've noted in your question. This appears to have been the case since some version of KDE 4. Possibly it is related to whether the icon theme is in a resolution-independent format.
iconSize system tray setting was added around plasma-workspace 5.9. Prior to the addition of this setting,
qml files had to be edited.
For a standard plasma panel, open
$HOME/.config/plasma-org.kde.plasma.desktop-appletsrc in the text editor of your choice. If you are using Latte Dock, open the
$HOME/.config/latte/*.layout.latte that corresponds to the layout you are using.
Look for the entry that corresponds to the system tray. It will look something like this:
Then scroll down until you see something that looks like this:
# is a number that refers to one of the following options:
0 ~ Small
1 ~ SmallMedium
2 ~ Medium
3 ~ Large
4 ~ Huge
5 ~ Enormous
To see the changes log off and on. Or, in a terminal, kill and restart
killall plasmashell ; sleep 1 ; kshell5 plasmashell
killall latte-dock ; sleep 1 ; kshell5 latte-dock