Investigate what’s called a dry-brush method.
Personally, I use 2” chip brushes that I’ve notched the bristles, a bit like layering hair.
I would use three similar colors of brown & go through the stair case with one color at a time, let dry &
hand touch-up with small artists brushes. The butt-ends are tough & I would mask the wall with painter’s tape.
Here's a great post on painting a wood look.
I have seen graining tools, also.
Here is a great post on Hometalk on how to do it: https://www.hometalk.com/11044950/diy-make-your-painted-staircase-look-like-real-wood-again?expand_all_questions=1