This thought experiment is yet another one from the liberal economic orthodoxy that assumes no deception or opacity or structural inequity, treats every human being as an "econ" that has perfect or near-perfect information and operates coherently, and leaves out the roles of collectives and institutions in favor of seeing every outcome as an aggregate of decisions made by individuals.

Especially in the modern interconnected economy, we are far removed from the actions, and we are subordinated to the modes of production we live under. Do recall that there have been dozens upon dozens of large experiments, just in the past century, where people strove to set up a system that would look out for the drowning children, prevent most of them from getting to the point of drowning in the first place, and incentivize everyone to use their available mental and physical resources to intervene in the rare occasion that someone got missed. These are known as socialist projects/nations/governments. And while academics in the capitalist world were thinking up abstract thought experiments to get people to acknowledge and embrace their complicity, people in socialist governments were actively managing resources to eliminate homelessness, starvation, extreme poverty, and even disease burden.

As soon as you become aware of your instrumentality in causing preventable harm to another human, you have a prerogative to orient yourself towards minimizing or preventing that harm. But you are not compelled to give up all your agency in the interest of things that lie largely outside your control: remember for instance that famine is not something that could merely be solved by charity, but is structural. The scenario presents you with a false dichotomy of either giving up all your resources (= personal agency in life) or being identified as the sole cause for the harm.

Orient yourself towards separating yourself from the capitalist system, and either undermining it from the inside or attacking it from the outside. Changing the system will do far more good than all the money in circulation being spent on charity.