Radio amateurs shoot for themselves the radar of the sky. The photographs show geostationary satellites.
Photographs aren't radar.
Some satellites are visible in photos of the night sky due to reflecting sunlight, Some rotate in such a way as to reflect light and then capture it with a sensor (i.e. like a camera). Other's don't rely upon sunlight at all.
Also, Geostationary satellites are in good positions for time lapse photos with fixed cameras as they remain in the same apparent location and thus the light can build up. Other satellites would be faint streaks.
As if they also hang in place, like geostationary satellites.
They don't. They go in several orbits, with a period of roughly half a day.
If they actually flew, we would see them in terms of brightness and size - about the same as the satellite that was moving.
On what basis do you claim this?
What satellite is shown in the video? How does that satellite compare to the GPS satellites?
From what I can tell, the only objects seen moving in that frame are the sun and moon.
These objects are very large, and quite bright. That makes them very easy to see. They have an angular size of roughly 0.5 degrees.
On the other hand GPS satellites are quite small. From my brief research, it appears they are 2.5 m wide. Do you really expect to see something that is 2.5 m wide at a distance of 20 000 km?