Here’s the bad news: There’s probably crap in the squirrel cage blower chamber, especially if the mice chewed through the filter.
The good news is that of all the chambers in the HVAC system, it’s the easiest to get to.
The bad news is that the fan tends to shred nests and the food mice bring in, and shoot it over into the next chamber, which is the evaporator for the air conditioner.
The worse news is that if there’s any food storage going on in there, that food is going to enter the evap chamber as a fine spray of food particles, and it’s going to form a layer of growth medium on the bottom of the chamber. Then when you run the air conditioner, the evaporator is going to drip water on the growth medium, and you’re going to get more maggots and a smell that isn’t going to go away without a lot of work - and unless you do it yourself, it’s going to be expensive. If you do it yourself, it will only cost you a bottle of Chlorox spray, some water, and several hours of rather disgusting work.
What I’m driving at is that before you run the HVAC system again, you should make sure there isn’t anything in the blower chamber. If you dive under the dash, you should see the motor - it’ll have a wire harness hooked up to it, and be held in with 3 small bolts. Just unplug it, then unscrew the 3 bolts, and it’ll drop right out. Make sure it’s clean (some dirt may be on the blades, but no mouse hair or food bits). If there is crap in there, and you caught it in time, it shouldn’t have blown much of anything over to the evap chamber, which will save you a lot of disgust and headache.