Painting individual stair steps

Hello dear people,

I have the following case and am hoping for your help.

I bought a house in which a harp staircase with, I assume, beech steps is installed. One of them had to be sanded down because it was totally messed up.
What should I use to varnish it again to match the color of the others?
I assume simple parquet lacquer is not enough since it would still be lighter then. What have the other steps been treated with?

Attached is a picture.

Thank you in advance

That is hardly possible to say from the photos, as there are myriads of possibilities. A specialist might be able to take a look on site, but they usually don’t do that for free (or very rarely). One thing I can tell you for sure: if you leave it as it is, it will of course darken over time. Was sanding it such a big effort that sanding everything down is completely out of the question? Then you can also choose the new color scheme yourself.

Thanks in advance for this answer. I have already tried to figure it out myself.

Whether they are stained and then painted or just painted.
I only have this one step.

Yes, there are a total of 28 steps and I already spent 1.5 hours on one step. After the complete renovation of our house, I really don’t feel like sanding everything down anymore. I actually abandoned that idea after that one step.

Especially since it really looks bad and untreated. What do you think are the most common methods for a semi-detached house from 2001?

Unfortunately, I forgot exactly what the stair builder told me. There are closed-pored and open-pored woods. Depending on that, you can oil and stain them or rather not. If I remember correctly, beech is one of the more closed-pored woods that you can't oil and stain very well. If the stair builder kept that in mind back then, it is probably lacquered. But surely only someone on site who knows a bit about this can tell you for sure. Is it definitely beech?

I would say that now. I think that's the most common. I'm just assuming that. I'm only a roofer, but I hope I'm right. Somehow it just looks like clear varnish. The question is whether the sanded step will get the same color with simple clear varnish. Expert or try it out....