I am a concrete specialist and though I see a few honeycomb areas on the side (cosmetic), and the exposed aggregate tops (Deliberate to give you tread), I'm not seeing crumbling that would make you tear this out. I see a few superficial chips on the edges of the stairs . .Tell us more about the problems you are seeing and experiencing ..

Wood steps are a bad idea. You could probably stain these or face them with real flat stone / use them like a foundation for something prettier .. but it would throw off the rise at the top - is the concrete on the porch slab okay?

You did not ask but have you considered fatter / chamfered posts to hold up your roof - you have so many charming details here and these are not to scale ..

Ok - I understand. Looks to me like the bottom "landing" / path with one more step down to the walk, is the only thing that needs to be repoured. The stairs are fine. Not pretty as you might like, but structurally fine.

This is some rough formwork, and indeed, it isn't surprising that they wanted to sell you more so it would look all the same, but they can demo the path and the landing (below the stairs) - then, drill into the existing face / base of the stairs - below the tread / where adjacent to the landing) and epoxy new rebar into that area. When they pour the new path, / landing, they will be connected where they say that they are not.

If you demo just the landing and the path, and place rebar as discussed, then pour the new landing / path (for much much less) they will be connected by rebar.

I nearly can guarantee that the stairs are not heaving higher - they are too big and solid and heavy to heave / and they are on some original foundation /stone that looks to be quite historical (how old is the house?). What you are seeing is the different settlement / heave rates between the walk / bottom landing (these shallower concrete landing areas below the stairs are moving - will move every year because they are thin and move with the ground underneath them). The stairs are unlikely to be moving - or not moving much).

They weren't tied to the bottom landing because of this freeze thaw issue. You would always put a control joint here for that reason, even with the rebar tie. The heaving under the path and landing will always be much greater - you can dig earth out and put down more sand beneath them when you pour to try and isolate it .. but generally, the shallowness of the walk means you have more movement there as a given -

You can put a bigger control joint with a prettier connection between the two (even with the epoxy rebar to try and keep the landing at the same height). The sides weren't finished nicely, but they aren't structurally a problem. In fact, with some concrete stain in one of the stone colors, and a little fresh epoxy mortar used like stucco on the ugliest "popcorn" area of the sides, you could make the under stair sides look very nice.

If you want to incorporate the flagstone cap (as if you had budget for that), it must be on every surface (why you need room between the entry door and porch landing as is) so the riser height is consistent. If you placed them on the porch, and the treads, you would then want to pour the bottom landing concrete higher than it was before / more height than now to keep the riser heights consistent throughout. Any new pour there will "fill the gap".

ps - I'm sure the stairs are connected to the foundation of the porch by rebar - keeping them a consistent distance from the top landing/ porch. The rust around the stair railings tells me this has been working for many years - you do not have a structural stair problem. You have someone trying to sell you more than you need.

ps - the stair foundation may not be structural like a builder would do them today. However, the presence of the blocks (no mortar here being a good thing - dry laid block has made some of the strongest walls in Europe that have stood for centuries -usually it is the mortar that cracks from heaving) and the history of the stone sides tells me this foundation has stood the test of time in your climate with this house. The concrete on top is not an issue - it is the connection at the bottom that needs work - that can be tackled by replacing only the bottom landing and the 4" - 6" deep walk / path concrete - much less concrete material if you leave the stairs = much less cost.