The current silicon ingots are amazing - cylinders a foot and a half in diameter and maybe six feet long. They are handled with cranes.
The ingots are so large and the chips so small that there isn’t much waste. The edges are often used for test patterns.
The chips don’t have to be rectangular, but it’s easier, because they are separated with diamond saws or wire saws, which cut straight lines.
Some companies make photosensors in weird shapes using ultrasonic cutters.