Beautiful space.

I would have the timbers all go the same direction for cohesiveness.

Rob, Since this already reads with so many horizontal elements - the brick, the stair risers read that way because they are open, and even the floor adds to this. I would be tempted to keep everything horizotal - the screen, the door, the railing.

I love vertical wood screens, and if you line / space the elements up with the open stair, it could work. The door that rolls should then also be vertical. If you keep those two things consistent, the railing ican go either way - The railings are going to go on a slope horizontally, so if you use a vertical screen, I think vertical rails could work too - either will be fine.

Thanks for the lovely comments.

@libradesign the sliding door storage space is going at the back of the apartment on the second floor. I have attached the back of the apartment for your info.

I am going to remove the balustrade on the stairs and replace it with the floor to ceiling vertical timbers. I am also going to replace all the balustrade on the second floor with a more industrial style steel wire strung between stainless steel finish. So you think the wires could be strung horizontally and the sliding screen and timber screen can have vertical timbers?

I really appreciate your advise :)

I think keeping like things alike in different areas of the apartment does help with unity in the long run. Have you consiidered using wood on the top railing that intersects with the wood coming from below?
I've seen some really interesting 2x2 used with 2x2spacing so that at the intersections it steps back / makes a neat contemporary lattice effect. You might run your vertical wood all the way through and up and then add /intersperse the horizontals.

Depending on the use of this upper area, you may really need more of a wall here than a rail - a half wall / pony wall with a wide top rail is much more functional in a room like this - you can put furniture against it, display objects on it, make a desk of the top, it makes the room more private as people come up the stairs . . . a tighter lattice screen here will be a feature and feel more like a "wall". When you see where your verticals are going to fasten, why not run them past the fastener location and let them be the structure for what you do above . . . .

Take a look at the screen on the window here -
a tube steel frame with 2 x 2 ipe https://www.houzz.com/discussions/is-the-material-on-the-frame-made-out-of-wood-dsvw-vd~599356

i feel comfortable about using both horizontal and vertical together in the same space....especially if the furnishings will have a minimalist look. beautiful space, lucky you!