Renovation of concrete stairs

[Odda]

We have a staircase built in 1955 that has seen better days. Unfortunately, it is impossible to find someone who can help me tear it down and build a new one. We have therefore discussed renovating it. I have knocked off all loose surface layers and pulverized concrete. What remains seems completely solid and stable.
My question is whether it is a good idea to renovate. The plan is to build a form, apply plenty of primer, cut reinforcing mesh, and cast a new surface layer (about 3-8cm).

 

[Stefan N]

What does it look like underneath? Presumably, the reinforcing has started to rust if it's that bad.

 

[Odda]

What does it look like underneath? I guess the reinforcement has started to rust if it is that bad.

The reinforcement is visible in some places on the underside. I've tapped them with a drift pin and they seem to have only surface rust. I plan to rust-proof and mortar in.

However, there are white salt deposits on the underside.