The video is very useful, thanks! With that I can reproduce the issue: when you create a new Position keyframe for the Z axis, the X and Y axis also get keys at that frame, but their new tangents are set such that the curve for X and Y does change a little bit around that keyframe, even though the X/Y values at the specific frame have not changed.
To me this feels like a bug in how the new tangents are calculated. Maybe, maybe, it is a limitation in how a Bezier controller with "Auto" tangents works, but the issue also happens if you set the first and last keyframe tangents to "Spline" before inserting a key in between.
In fact you can see the same issue if all you do is to move the timeslider between the first and last keyframe and rt-click the timeslider to create a new key (i.e. without moving the object). Even with that the curves between the first key and this new one do change a bit. Same for the curve between this new key and the last key.
The best suggestion I have is to afterwards delete the new X and Y keyframe and only keep the new Z keyframe. That will restore the original curve for X and Y.
Martin B
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