The roof structure rises by almost 2 cm upwards!

Wood mainly reacts to moisture and not so much to temperature. Temperature-related expansion can generally be neglected. If the panels were the cause, they would somehow have to overcome the screws, as these are connected to the substrate. It is not only the last piece of the panel before the first screw that expands. Even an OSB panel reacting to moisture (which is excluded with typical OSB 3) would rather warp between the screws and move away from the construction than lift off entirely.

It is a mystery to me, but I'll take a stab. The roof frame is standing. However, the wooden ceiling is bulging. Why? The solid wood in it is getting damp because the [OSB] stuff on top is sealing it off! Possible?

Maybe the beams also got damp during construction, absorbed water, weren't properly dry. OSB stiffens the beams on top and they warp while drying.

But that's just a guess. What does the insulation under OSB say?

The roofers must use technically dried battens (for wood protection reasons). The drywall installers do not. Due to the low humidity, the counter battens installed by the drywall installers shrink especially in winter. This causes the cracks.

The roofers must use technically dried battens (for wood protection reasons). Drywall installers do not. Due to the low humidity, especially in winter, the counter battens installed by the drywall installers shrink. This causes the cracks.

This is not wrong, but it can never lead to a lifting of the roof structure. Just think about how much weight is behind it. An OSB board or the screws used can never cause that. Moreover, the expansions caused by drying/swelling are not in the range of 2cm, unless wood from marine storage was used.

Sorry, I do not see a raised roof truss. I only see a suspended drywall ceiling whose substructure has shrunk. In the areas where cross battens create an additional suspension, the shrinkage adds up.