They sell a pc called a stairnosing.. And you use the same wood on the stairs as the foor..Its a curved trim pc that is on the edge and place pcs beyound that.
If you can find a stain to match they also sell premade pcs that you cut to size.. GL
You should be able to buy new stair treads in the same material as your floors.
same material on the steps. just takes a little ingenuity to do the job.