Some of the Korg standalone synth apps respond to midi, between apps. Some only to bluetooth midi from a external device. In the full version of Gadget you can use your mono-poly app with midi. Likely the Korg synths don’t support auv3 because they are competing with Cubasis and others with their Gadget daw.
My iPolysix app for example does not work with ‘inter-app midi’ but the Korg iOddysey does. Which would still mean you’d have to send midi from another app to get it to run inline with other parts.
The full version of Gadget and all the synths in it do work well with AUM.