On a Monday evening in November, Dorri McWhorter, the chief executive of the Y.W.C.A. Metropolitan Chicago, got a phone call from a representative of the billionaire philanthropist MacKenzie Scott. The news was almost too good to be true: Her group would be receiving a $9 million gift.

Between the pandemic and the recession, it had been a difficult year for the Chicago Y.W.C.A., which runs a rape crisis hotline and provides counseling to women on jobs, mortgages and other issues. Money was tight. Ms. McWhorter shed tears of joy on the call.

Similar scenes were playing out at charities nationwide. Ms. Scott’s team recently sent out hundreds of out-of-the-blue emails to charities, notifying them of an incoming gift. Some of the messages were viewed as possible scams or landed in spam filters. Many of the gifts were the largest the charities had ever received. Ms. McWhorter was not the only recipient who cried.

All told, Ms. Scott — whose fortune comes from shares of Amazon that she got after her divorce last year from Jeff Bezos, the company’s […]