Attic, which flooring to install?

Definitely not thinner. Your rafter spacing is too wide for that. Better take 24mm. I would forgo a cross battens, it doesn't help. Under OSB, one could consider a cross battens for circulation purposes, but even here the effectiveness is disputed; in my view OSB is generally unsuitable.

And I also wouldn’t choose the worst grading, the better quality is easier to install and later you can even walk on the [Spitzbuben] wearing socks without getting splinters in your feet.

Have the boards cut to length right away, so you don't have to saw much later. For example, 3m boards at 3×95 - 1 = 284 cm

No, exactly the opposite with the battens. Not as ventilation either but precisely because of the large rafter spacing. If a lot is stored, I would prefer that.

We installed [ESB Platten] with 22mm thickness here. It was easier than tongue and groove and looks neat.

Tongue and groove. It breathes. That's how it is here.

Here also ESB

Hi, one more question.
What do I do with this annoying 4.5 cm thick beam that runs lengthwise exactly through the middle of the attic?
Even if I use 28 mm tongue and groove boards, this beam is still 1.7 cm higher and therefore a toe breaker.

When laying them, should I lay them all parallel and always end on such a rafter, or stagger them like a floor? And then let some boards end “in the air”?

And have “3m boards cut to 3x95-1 cm”? What is this -1 supposed to mean?