I can understand adding this directly could make the app lose his focus. After a quick search I have seen multiple solutions for this that could complement Open Stage. They are apps/scripts to translate OSC or midi messages to keyboard shortcuts in the host.
I will try some of these but if anyone can share how they work for them would be great as It seems logical many people are interested in using Open Stage to control both things at the same time, and a bridge could allow it. I guess some of the solutions will be better than others.
These apps use midi or OSC signals to convert them to keystrokes (not tested any of them ). Some of them multi platform:
Midi to keystroke
https://www.bome.com/products/miditranslator
This translate OSC to keystroke
Another one, this is the one with more internet references of people using it for that:
https://www.bome.com/products/mtclassic
Tutorial for using this app, borne, for midi to keystrokes:
Another one:
Other references:
https://www.muffwiggler.com/forum/viewtopic.php?t=117356
https://www.pgmusic.com/forums/ubbthreads.php?ubb=showflat&Number=430438