Makes sense. That would indicate the sound is more likely coming from the heater core. But how cold are the nights where you live? Cold enough the AC drain area inside the car might freeze solid? The water that goes into the AC drain area doesn’t have any freeze protection. If so, that could explain why you don’t hear any sloshing until you’ve been driving awhile.
I’ve had air pockets in the cooling system on my Corolla that cause a sort of sloshing sound when the heat is on, but its not related to braking. Every car design is different though.