Replacing stair steps

Not final at all.

However, we have an offer for a complete staircase with railing in wood with solid oak steps, which appeals to us very much.

But as said, it is not final yet.

We have, however, an offer for a complete staircase with railing in wood with solid oak steps, which appeals to us very much.

Does the offer include only the new staircase or also the professional removal of the old one?

That is actually the crucial point. Even from a logistical perspective, the removal is no fun. Have you considered the consequences of "carrying it yourself"?
And: the helpers should definitely be insured against accidents (and trained in accident prevention regulations). You can't just lift out the steps like shelves.

P.S.: I just asked Kenngott about this. For the removal, two men would need to be deployed for two days (mind you: two men for whom this is daily routine), and of course, support measures would be necessary.

I would then start at the top and support each step below. Has anyone done that before? Does it work the way I think?

The idea of literally removing the old one step by step and installing the new one has something somewhat amusing about it. In my mind's eye, it’s playing out as an episode of ToolTime with Benny Hill as a guest star

What a staircase builder offers for a still or already empty stairwell is a completely different matter.

Also because of the expansion, we are in talks with a company. Parallel to this, I am looking for a Plan B, whether the steps can be worked on (painted?) in some way and fitted with a new railing.

Take a look at the so-called Steinteppich. There are different ways to "change" a staircase.

As someone already said, presumably five-figure amounts are being invested in a depreciation here.