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Why not just use VSync?

If I am not too much mistaken, because on some hardware (mobile), there is no vsync feedback.

vsync feedback support has to be queried (look at vulkan API/wayland API). Usually it is called "presentation" something.

How would I do that? I think there is any such function in the Win32 API.

Yes, I think you basically have to use a DirectX swap chain to get vsync presentation.