Construction scheduling - Who has to create it? General contractor, site manager?

What does the site manager do, if not coordinate the trades (to which the schedule undoubtedly belongs)?

What does the site manager do if not coordinating the trades (which doubtlessly includes the scheduling)?

In this case, he will be managing the construction on site.
No idea: I didn’t hire him.

This is a special arrangement here. Anyone who agrees to it will have to come to an agreement beforehand.

In my opinion, a construction supervisor (BU) instead of a general contractor (GU) would be sufficient to ensure that everyone can fulfill their role properly.
Maybe one should ask the architect what he has in mind. Includes all trades and coordinates them well, for example. :)

Cleared - Site manager creates a rough construction schedule

What does the construction manager do if not the coordination of the trades

Managing construction, as the name suggests ;-) The construction manager is the interface between the planner (often himself) and the foreman. He checks compliance with the plans, signs off timesheets, etc. That is a task in daily business. The conception of the basic procedure, i.e. that the excavator operator must come long before the roofer, was already a planning task and is long completed when construction management begins. The construction manager is urgently needed when there are pipe bursts or bodies found on the construction site (both of which the architect did not include in the plan), when the concrete mixer is stuck in traffic, the crane was stolen, or someone has to chip away something that his predecessor made too tight. So less as a process planner, but as a crisis manager when reality behaves out of plan. And after all, someone has to put their stamp on it when everything has turned out as it should.

Construction management, as the name already suggests ;-) The construction manager is the interface between the planner (often himself) and the foreman. He monitors compliance with the plans, signs off on time sheets, etc. This is a task in daily business. The conception of the basic procedure, that is, that the excavator operator must come long before the roofer, was already a planning task beforehand and is long completed when construction management begins. The construction manager is urgently needed when there are pipe bursts or bodies found on the site (both of which the architect did not include in the plan), the concrete mixer is stuck in traffic jam, the crane was stolen, or someone has to chisel something off that his predecessor made too tight. So less as a process planner, but as a process rescuer when reality behaves off-schedule.

He documents the construction progress, among other things with photos.

Thanks for your answers ... My question was partly rhetorical. IMHO the site manager is also responsible for the construction schedule (in addition to the activities you mentioned). But whether/how this is officially regulated on site -- no idea. I transfer this view from my understanding of the project manager in general to the site manager, who is also "only" a project manager.

BTW. In our developer house, there were two site managers. One from the developer and one from the main contractor commissioned by the developer. But it didn't work out very well.