Currently MenuToolGroup gets set a semi hard-coded image in Apex.
.oo-ui-tool-active .oo-ui-tool-link .oo-ui-iconElement-icon { .oo-ui-background-image-svg( '@{ooui-default-image-path}/icons/check' );`
We should replace this by an IconWidget instead and show/hide it depending on the theme.
Same applies to MenuOptionWidget (in Apex) and CheckboxInputWidget (in WikimediaUI).