I think I've found the answer to my own question. It looks like the 1950 Ray Bradbury short story, "There Will Come Soft Rains," which has its own Wikipedia page that includes this description:
The story begins by introducing the reader to a computer-controlled house that cooks, cleans, and takes care of virtually every need that a well-to-do United States family could be assumed to have. The reader enters the text on the morning of April 28, 1985 (changed to August 4, 2026 in later printings), and follows the house through some of the daily tasks that it performs as it prepares its inhabitants for a day of work. At first, it is not apparent that anything is out of the ordinary, but eventually it becomes clear that the residents of the house are not present, and that the house is empty. While no direct explanation of the nonexistence of the family is produced, the silhouettes of a man, a woman, two children, and their play ball are described as having been burnt into one side of the house, implying that they were all incinerated by the thermal flash of a nuclear weapon.
Thanks to anyone who was looking for an answer.