The FDA routes submissions based upon the primary mode of action. For inhalers and similar types of devices, the primary mode of action is as a drug. Therefore, the applicable drug division will review first and then devices will become involved. For other products, the primary mode may be a device and a drug might be secondary in affect. An example is the addition of drugs to stents. The product is a device first in this case. For Europe the inhaler is a device, but classification is dependent upon if the manufacturer is selling the inhaler to another company for charging with drug or if the inhaler is already loaded with drug. It sounds like your company is loading the inhaler with drug and therefore treatment by the applicable competent authority would be similar to the FDA's approach.
The inhaler is not just packaging, because it dispenses measured doses. Believe it or not, a cup with lines for each milliliter is also considered a device. The lines may be different dependent upon the viscosity of the liquid. Inhalers are even more complex and there are many considerations that are well beyond the scope of liquid and pill formulations.