Electric velcro
Build a panel with a grid of induction loops behind it, then cover it in velcro fabric. Electrical items like LED lights can have a corresponding induction loop covered in the complementary velcro fabric, and thus lights, switches, sockets, etc. can be freely repositioned on the panel and connect to the electrical network via induction. Theoretically a whole room could be made like this, allowing electrical devices to be ‘stuck on’ (vs ‘plugged in’) anywhere.