What if the houses realizes that the inhabitants are gone in "There Will Come Soft Rains"? What would it do?

The house will never realize its inhabitants are gone. It does not have consciousness.  The house is a robot.  It is sort of like plugging in your television.  You could leave your television on and never come back.  Your television is not going to realize you are gone and turn itself off or take some other action. It is a television.  It cannot think.

The house is doing what it is programmed to do.  It will continue as long as it has power and resources or does not become corrupted.  This means it will keep making breakfast until there is no more food. It will keep making announcements until no more are registered.

The house does seem to have some sense of self-preservation, meaning it wants to remain “alive” and functioning.

Until this day, how well the house had kept its peace. How carefully it had inquired, 'Who goes there? What's the password?" and, getting no answer from the only foxes and whining cats, it had shut up its windows and drawn shades in an old-maidenly preoccupation with self-protection which bordered on a mechanical paranoia.

Again, although personification is used here this is really just programming. Somewhere in the house’s programming it has been told to close itself off if it gets no response.  There is no artificial intelligence at work here.  The house is not thinking and adapting.

When a tree bough breaks through a window and knocks a can of solvent onto the stove, the house tries to put out the fire.

The house tried to save itself. Doors sprang tightly shut, but the windows were broken by the heat and the wind blew and sucked upon the fire.

Unfortunately, the house does not have a chance.  It has sprinklers, but the fire is out of control.  The house will never realize its family isn’t coming back.  It burned to the ground.