You are right in emphasising the way that, as you call them, "human" verbs are used in the story to portray the extent of technological development and how we are presented with a fully functioning house in this great short story with no need for humans to do anything. Consider how the voice-clock "sings" and the voice tells the absent humans all they need to do:
"Today is August 4, 2026," said a second voice from the kitchen ceiling, "in the city of Allendale, California." It repeated the date three times for memory's sake. "Today is Mr. Featherstone's birthday. Today is the anniversary of Tilita's marriage. Insurance is payable, as are the water, gas, and light bills."
With no human characters therefore, this story is an ironic reflection on the strengths and weaknesses of human nature. It is also a dire warning about the limits and dangers of technology. By showing us a house that operates without the need for humans to do anything, Bradbury presents us with a future level of technological sophistication that amazes us - until we remember that technology has literally done away with the need for humans - both in the sense that the house does everything, but also in the sense that technology has destroyed mankind. It is this message that the use of "human" verbs emphasises in the story.