What I’m about to describe is my drone’s parachute release system. :)

To release something soft, you would typically have a concave surface or channel on the underside of the drone. Like a bowl upside down, or a pipe cut in half into U-shape and placed upside down. Obviously, for a water balloon - no sharp bits allowed. A parachute requires a wide strap to hold it, tensioned with rubber or made of rubber. Since a balloon is elastic, I think a balloon could do with an inelastic strap.

Anyway, the strap would end at some distance with a solid endpiece, the purpose of which is to distribute load. It might be triangular, circular, anything. The endpiece would end with a loop of string. The loop of string would go though a hole in a holding surface (don’t pull knots through a hole, they can get stuck). On the other side of the holding surface, a pin bent of wire would lock the loop of string. Tension and a slight bend in the pin would ensure it won’t come loose with vibration. Once a servo pulls the pin out of the loop, the weight of the object being released (or the elastic force of rubber) would pull the loop of string out through the surface. The strap would come loose and the object would drop out of its upside down bowl or channel, releasing the parachute (or balloon).

However, this is just one out of dozens of possibilities. It’s relatively beginner-friendly however, hard to get wrong.