The default transform track type in Sequencer/Timeline is “Absolute”. This means that the object will snap to the position evaluated by Sequencer. If you hit the +Track section on the Transform Track you can use a “Relative” transform instead. Relative tracks can take the object’s current position into account instead of just snapping to the specified value.
The relative transform will need to be blended with an absolute section - I believe this video has the details on how to do it;
If you reverse the animation mid-animation it should go from it’s current position to the target without snapping.