They can be patched; see https://www.todayshomeowner.com/video/how-to-repair-and-resurface-concrete-steps/  No guarantees as to longevity but may give you a year or two.

You can also demolish, redesign and pour new steps. As Sophie says, make the landing wider and probably deeper too, and overall check for best dimensions.

You could also remove the railing and simply build a decking porch (in wood or Trex-type material), with handrails, ignoring the existence of the steps.

In the meantime, pressure cleaning the steps will really help. Maybe all you need to do is paint the steps until you decide to redo them. A nice, clean entry with painted steps and a good sized welcome mat will brighten the area.

I may be wrong about this--hoping Building Code experts here can confirm or not--but isn't it against Code to have a front door that steps out onto air, like in the OP? In other words, shouldn't the first landing be on the same plane or level as the front door threshold?

I think you should rip out those steps and put in something nicer. It's the first thing people see of the home, and sets the tone.

As long as it’s the same correct uniform height as the steps, and there is a 3x3 landing that you are stepping onto, it’s fine. Much better for snow and rain locations actually.

Like others said, there are many ways this can be done, you can patch and resurface, you can use cultural brick matching existing brick on the house, I just recently renovated the house and had similar concrete steps with broken corners etc, and to give you an idea this what I did to restore them

Good luck

Thanks so much! Amazing transformation. Approximately what was the cost for the step transformation in the pictures sent?