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 "empty" 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?

It's unfortunately more complicated than just finding a 2x9 shifter.

Pull ratios (the distance a cable has to "move" to shift from one gear to another) are different on road and mountain bikes groupsets (Acera is in the MTB range). Assuming you'd find a 2x9 with hydraulic brakes, they won't be directly compatible. There are adapters, but from what I've seen their price is in the same range as a Sora derailleur (the equivalent of Acera in road components). Not sure it's worth doing in this component range. (not true for for 7-9 speeds, see comment)

Also, there can be some incompatibilities regarding the fluids used in hydraulic disc brakes, if you mix the brands for the caliper (do you have Shimano or Tektro, is it mineral oil or DOT?) and the shifter, you will also need to make sure that fluids are compatible.

If you are on a budget, plan to buy a new bike next year and count on the sale of your current bike to buy the new one, take also in consideration that selling a modified bike is more complicated than a "stock" one.