A serpentine back is one of those details that costs a great deal and announces itself very quietly. Straight-backed sofas are quicker to frame, quicker to upholster and far easier to button, because every diamond sits on a flat plane. Curve the back in two directions and the buttoning grid has to be plotted onto a surface that is changing shape under it - each diamond slightly different from its neighbour, each button pulled to a different depth.
Get it wrong and the pattern visibly wanders. Get it right and nobody notices anything except that the sofa looks expensive.
The curved chaise at the end comes from the same instinct. A square corner would stop the serpentine dead; sweeping the seat round in plan lets the curve keep going until it runs out naturally.
Our master Indian artisans plot the buttoning full size on the finished frame before a single button is set, marking each position by hand on the curve itself rather than working from a flat drawing. It is slow, and it is the only method that survives the shape.