The easiest short-term answer is: continue using a Classic Component for your modal (i.e. not a glimmer component). Classic Components still support mixins.
Sticking to a classic component (i.e. the strategy described in Converting modals from legacy controllers to new DModal component API) will give you the cleanest 1:1 upgrade from the old controller-based system.
Longer-term, we will need to figure out alternatives to some of our core mixins. But we haven’t quite got there yet.