The pump is timed by the number of shims under it. More shims retards, less advances.
Am I correct in assuming that this timing is fixed through the entire operating range of the engine? Optimized for around 2000 rpm?
You are correct. There is no timing advance/retard for various RPM's.
Your engine is a "ZS" and is direct injected.
That engine sounds quite normal in the video.
Other things that can be construed as abnormal noises are the gear lash in these larger Chinese engines.
Due to having straight cut gears with lots of lash, the Cam, Counterbalance, and Start shafts, have a lot of gear clatter. And that too is normal.