This morning I discovered the cause, and worry has flown. It's a pileup of Inca doves roosting on the window sill. The bathroom window is up high enough that cats would find it hard to snag a dove off the sill; it's protected by bushes so aerial predators can't easily get to it; it's also out of a northwest wind (like the one overnight bringing in colder air) and gets the morning sun.
At first light this morning, I could just see a solid row of little gray lumps...later, with more light, I could see they were stacked like paperbacks on a crowded bookshelf, some actually on top of the others, all fluffed out, heads tucked in, keeping one another warm. In the early light, before the sun hits them, they look like little mounds of dryer lint. But they do move a bit, and "talk" a bit, so their feet scritch on the brick of the windowsill, and their tails may hit the frame of the screen, and the top layer, coming in to roost, may grab the screen before the dove tucks itself into the pile.
Though they appear so sweet and helpless, I've seen Inca doves "armpit" each other and also sparrows trying to feed in the same area. (The "armpit" maneuver: a bird raises its wing on the side towards the bird it wants to dominate/drive away, literally showing its "armpit." If the target of aggression doesn't move away, the dove will crowd it and then peck at it. Not all species "armpit." Both white-winged and Inca doves do. Some species raise both wings while facing a bird they want to dominate/drive away, but that's a very different posture.)