What happens to the entropy of the pre-existing information on a black hole event horizon as more mass falls into the hole? Does the old entropy stay the same as new bits of information are added to increase the overall entropy?
 A: I'm not a black hole entropy specialist. But I'm noting down some of my observations, which may be helpful for you.
Black hole entropy is related to the horizon area, $A$ of that black hole: $S_{Schwarzschild~BH}^{\left(Wald\right)} = \dfrac{A}{4G_N} + + 64\pi^2c_3(\mu) + 64\pi^2\gamma \left(\log \left(4G_N^2 M^2 \mu^2 \right) − 2 + 2\gamma_E \right)$ , where $A = 16\pi~(G_NM)^2$
[Source: Calmet, X., & Kuipers, F. $(2021)$. Quantum gravitational corrections to the entropy of a Schwarzschild black hole. Physical Review D, $104(6)$, $066012$.]
So if a bit of information (here I'm considering the information to be a bit of mass) is being added to a black hole, then the black hole mass and hence the horizon area will increase (according to the $2^{nd}$ law of black hole mechanics). So obviously, black hole entropy will increase.
Forget about the quantum corrections in the BH entropy for the time being (and for the easiness of the calculation and to have a physical intuition):
Let $m$ amount of "radially in-falling" mass (or information) has been added to a Schwarzschild BH of initial mass $M$. So BH mass will then be $M+m$ .
$\therefore S_{BH}^{new} = 4\pi G_N (M+m)^2$ , while $S_{BH}^{old} = 4\pi G_N M^2$ .
Hence, $S_{BH}^{new} \approx S_{BH}^{old} \left(1+\dfrac{2m}{M}\right)$ .
So the entropy has been changed, as we have seen from the simple-most consideration.
