I would like to stabilize a shot so that the background is absolutely still. Which settings lead to this result? The clip is 5 seconds long and the camera pans very little and slowly about 5% of the image area. The shot is not actually shaky. I have already tried many parameters, but the background is still moving.
Very difficult to answer without having the actual footage at hand or knowing what parameters you changed and how. Did you read the chapter about stabilization in the official manual?
I would start with selecting a high-contrast area in the background where there is the most shakiness. Then set Accuracy to something 10 or higher, *Shakiness to something smaller than 4. It is a lot of trial and error …
You may also look into what @Arkengheist did for her Lock-on Stabilization video. Perhaps this helps …
I succeeded with the effects:
Motion Tracker
copy keyframes in
inverted position to
Transform.
That, pinning the motion tracking to some feature you want to lock on to, or something like Gyroflow (if your footage has gyro data it can use), are the best way to do this at present.