Another flatbar to dropbar conversion noob
I think you are out of luck there.
There are expensive cable to hydraulic converters available.
You could get (equally expensive) 10 speed hydraulic brifters and use a 10 speed to 9 speed cable pull converter. This should work with your existing drivetain (you’d have an &quot;empty&quot; 10th gear).
But all of that would be a hack. Is the frame even short enough to be comfortable with drop bars instead of flat bars?