Except now you are going to argue...
Do you fly often without the battery?
Just stop - you have no idea what you are talking about.
Firstly, this has nothing to do with Newton's 3rd law, which doesn't have anything to do with weight, area or pressure. It is related to the differential form of Newton's 2nd law, in that the force exerted during impact is equal to the rate of change of momentum during the impact. And the rate of change of momentum is a function of the duration of the impact, which itself is a function of the rigidity and strength of the materials involved.
Soft materials, a category that includes birds, are quite compressible and so the impact lasts longer, the rate of change of momentum is lower, and the impact forces are lower. Rigid materials, including various drone components, are not very compressible; the impact duration is short, the rate of change of momentum is much larger, and the impact forces are much higher.