In the animation player i can add a track for the variable, i set the update mode of the track is continuos but when i run the animation the update is like the discrete case, so position_offset is updated only during the keyframes, not in between, the print output is something like this:
Look, i feel stupid but i found the problem: i tried to do the same thing in a dummy empty project and everything worked. Then i noticed than in my project i had this strange error when i added a keyframe:
I could still set the values but initially i always had this error.
What i did is:
1 delete all tracks with this variable, including the reset one
2 restart the project.
Now if i add again the track everything works as expected. So i do not know if something was corrupt or some kind of a bug or something else but now it works
Thanks @normalized for your help