Looking for advice in how to finish a concrete to carpet transition. We have burnished concrete floors throughout the ground floor, with tiles in wet areas and carpet in bedrooms. To keep simple consistency I would like to have concrete stairs which open onto the sitting room. How would you transition from the concrete stairs (single straight run) to the carpeted sitting room?

We were thinking to have timber treads and risers but would prefer to not add a 4th flooring in the house, and have been told it'll cost 9-17k to have wood fitted.
We definitely do not want carpeted stairs.