Put another way, in the long run under market economies, does philanthropy reduce the power of altruistic actors and increase the power of non-altruistic actors? If not, why?

I think it's true that donating €10,000 may reduce my personal power/influence compared to keeping it in the bank. But I think it's essential to keep in mind that my €10,000 wouldn't be burned, it would "increase the power" of the beneficiaries/recipients. Given the diminishing returns on wealth, I expect the extra power the beneficiaries receive is more than the power I lose, so overall power transfer is positive-sum, and from someone relatively rich (like me) to someone relatively poor.

Another IMHO extremely important consideration is that money will be spent on something eventually. So if I buy something on Amazon instead of giving it to charity, I'm transferring wealth/power/influence from people in extreme poverty (partly) to Jeff Bezos, and conversely, if I donate to charity instead of buying something from Amazon I would do the opposite, which seems to me a better form of wealth redistribution.

(Also of course this ignores the many other positive effects of giving to effective charities, besides "power" transfer)

I think the transfer from the philanthropic actor to the charity preserves the “altruism” of the resource-utilizer so there shouldn’t be a net loss there unless you think gains due to charity don’t accrue as quickly as capital gains in the private market. So I think then the question kind of reduces to give now or give later. Unless there’s some belief in concentrating resources being inherently better than diffusing them.

You are correct. Through the safety net funded by altruists, egoists can afford lower taxes and receive greater benefits. As a result, egoists get stronger and altruists get weaker. That is, those who benefit themselves through charitable giving or don't give at all will become richer and stronger, while those who give to benefit society will become poorer and weaker.

Even if you think that the effects caused by your charity will grow exponentially, this not only still holds true but even more so. For these effects clearly manifest as a transfer from the altruistic to the selfish. Therefore, if this transfer grows exponentially, then the selfish will become more profitable and the altruistic will become more impaired.

This, in short, is part of the evidence for the argument of socialists in the broad sense that improving society requires collective action, not individual charity. Even social democrats advocate improving the social safety net through taxes and state benefits, not through tax-deductible subsidized charitable giving.