In the well fed state, major fate of glucose-6-phosphate in tissues is:

The uptake of glucose into  the  liver through GLUT 2 is independent of insulin. In the well fed state, the concentration of glucose entering the liver increases, so does the rate of synthesis of glucose-6-phosphate. This is in excess of the liver’s requirement forenergy-yielding metabolism. So, it is used mainly for synthesis of glycogen. In both liver and skeletal muscle, insulin acts to stimulate glycogen synthase and inhibit glycogen phosphorylase. Harper 30th edition pg -148