Lower the ceiling? How high to build the ceiling wall?

I would never undercut the ceiling, since the room is already not particularly high. Every centimeter of height in an all-purpose room brings "more" feel-good atmosphere. If you absolutely want a permanently installed indirect lighting, then use those paintable polystyrene moldings that finish the walls upwards and house LED strips. In the children's apartments, we have the classic round recessed lights, often called "spots" here, installed in the ceiling. They provide decent functional light, which practically plays no role in living.