What is the meaning of the quote “no doors slammed, no carpets took the soft tread of rubber heels” from the short story "There Will Come Soft Rains"?

"There Will Come Soft Rains" follows an automated house in a world where humanity has been destroyed by nuclear war. Bradbury opens this short story with the following passage:

In the living room the voice-clock sang, Tick-tock, seven o'clock, time to get up, time to get up, seven o'clock! as if it were afraid that nobody would. The morning house lay empty. The clock ticked on, repeating and repeating its sounds into the emptiness. Seven-nine, breakfast time, seven-nine!

That is the very first paragraph that opens this story. What, then, does it establish? What we see here is a house continuing to run according to a preset routine, as if it still held human residents. This then is the tension that shapes the story: the house is a work of technology, created to serve a purpose. But in a world without humans, that purpose has now been rendered obsolete.
The quote you are asking about reflects that same tension. It is invoked in the context of that same routine which introduces the story, a routine intended with a family in mind. The house had been created to serve humans, but there are no humans left. The house stands empty, but it still goes on as if it isn't. This is the tragedy of the house itself, even if the house itself is unaware of the tragedy of its own existence.
Through his use of rich descriptive passages, Bradbury is able to depict the aftermath of a nuclear war where humanity has vanished and its technology is all that appears to have survived.

At the beginning of the short story "There Will Come Soft Rains," Bradbury illustrates the everyday automated routines of a technologically advanced smart home, which operates daily functions to make the anonymous family's life easier and more efficient. Despite the automated wake-up call and the impressive breakfast, which is produced by sophisticated mechanisms, the family is eerily absent. Bradbury emphasizes the family's absence by writing, "But no doors slammed, no carpets took the soft tread of rubber heels" (1). While describing the elaborate mechanically-driven morning routine, Bradbury highlights the lack of slamming doors and stampeding feet, which are the typical sounds of an active family getting ready to start their day. As the story progresses, the readers discover that the only thing remaining in the wake of a nuclear blast zone is the technologically advanced smart home, which continues to function despite the fact that the family it caters to has died in the blast.

To understand the meaning of this quote, let's first put it into some context. It is one minute past eight in the morning. In the story, this is the time when parents leave the house to go to work and children leave to go to school. As such, we would expect to read about the slamming of the doors and the tread of rubber heels of the carpet. This would indicate to the reader that people are leaving the house to start their day.
However, in this quote, Bradbury is telling us that these sounds are missing from the house today. The purpose of this is to highlight the silence in the house. He wants the reader to understand that these people, who should be making noise as they get ready for work and school, are not there. He is therefore highlighting the sense of loss.
Looking deeper, Bradbury is also highlighting the darker side of technology. Thanks to the atomic bomb, this family has been eradicated and will never again slam a door nor tread on the carpet. Only their automated house remains, but it has no idea that the family will never return.

Despite the fact that the automated house in Ray Bradbury's short story "There Will Come Soft Rains" has started the day by making announcements and cooking breakfast, there is no sign of humans. In the first paragraph the narrator indicates that "The morning house lay empty" and later that "no doors slammed, no carpets took the soft tread of rubber heels." Instead of describing human characters, the narrator makes the house itself the main character. It is not revealed until well into the story that there has been an atomic blast and that the house is the only one still standing "in a city of rubble and ashes." The humans who inhabited the house, two parents and two children, have been incinerated in the attack, but their silhouettes remain on the charred outside wall on one side of the house, reminiscent of photographs taken in the days after the first atomic bomb was dropped on Hiroshima in 1945.