For those of you wondering: It was a busted sump pump, not an actual busted pipe. Which is good because a busted sump pump is easy to fix, whereas a busted pipe (depending on where it is), not so much. We broomed out much of the standing water ourselves and then let the pros come in and handle the rest, and now we’ve got three very large blowers downstairs drying the place out (see picture). And of course, now we have a new sump pump.
We had some water damage to stuff we had stored down there but not as much as there could have been, and we used the opportunity to junk some stuff we’d been meaning to get rid of anyway. We’ll have to see what the final bill is, but overall, if you’re going to have a domestic disaster, this seems the way to do it.