Why does black hole grow? How does Einstein Field Equation describe this process? [duplicate]

Let's talk about this in the reference frame of an observer far away from the black hole.

When an object travels near the event horizon, time flows infinitely slow. It gets closer and closer to event horizon but never reaches the event horizon. It never reaches the singularity to contribute to the singularity's mass.

But we can observe the black hole grows. Why?

This is what I think. When more and more objects accumulate near the event horizon, we need to re-calculate the center of mass and the equivalent point mass of the black hole. Then you will find the Schwarzschild radius is now larger. It instantly "swallows" everything that was near but outside event horizon. Are my thoughts correct?

How to describe the dynamic process of black holes growing by Einstein Field Equation, supposing you rigorously keep track of every object rather than treating them as an equivalent point-mass?