The long and short of it is that Kamala was part of the same campaign committee as Joe, with respect to the donations that had been made. There was around $250 million from donations at the time. Because they shared the same committee, it was highly likely that there would be no complications in transferring funds to her as the new Presidential candidate.

For anyone else to become the new candidate, however, Biden would have to offer donors the option for refunds (which the Dems absolutely did not want since they knew it would leak away massive amounts of that warchest). The remainder could still end up going to the DNC, but only a fractional portion of that could then be sent back to a new candidate. That would still have been relatively sizable, like 30 or 40 million, but not near the quarter-billion Biden had built up.

This also doesn't touch on PACs which had hundreds of millions generated for Biden, but that may not have been therefore usable for a new non-Harris candidate. I think some of these still faced complications even with Harris.

Regardless, the huge held-breath pause that the Democrats seemed to take as it became clear Biden was being forced out was because of the internal maneuverings regarding the campaign funds and how they could keep their hands on it all.