Mr. Scott entered the 2024 race with a war chest of $22 million, and his campaign raised $5.8 million from April through June. In that same time, he laid out about $6.6 million, a significant clip — but most of it cannot be traced to an actual vendor.

Instead, roughly $5.3 million went to two shadowy entities: newly formed limited liability companies with no online presence and no record of other federal election work, whose addresses are Staples stores in suburban strip malls. Their minimal business records show they were set up by the same person in the months before Mr. Scott entered the race.