Seal / fill basement stairs leading to the house

Hello,

the area around the basement stairs has now been plastered.

I notice that the basement stairs are flush with the basement / the plaster at the bottom and at the top we have a gap about a finger's width.

Is that normal / can that happen?

How do I "fill" that so that over time I don't sweep all the little stones, dirt, etc. into it?

Best regards and many thanks!

So it looks different for us. The stairs are directly connected to the concrete.