In what way can an object move with the movement of the sun? That is, let it follow the movement of the sun.

Simple, erect a benchmark, measure the movement track of the shadow at the end of the day, calculate the angular velocity, then find a stepping motor and set it to the same angular velocity, and you can drive it as you want, without any automatic device at all. The advantage is that it can be tracked even if the sun doesn't come out. The disadvantage is that the sun runs in different seasons and needs to measure the angular velocity many times.