When pushed by a sticky piston, amethyst clusters do not break, but they drop 2 amethyst shards as if they were. By attaching an amethyst cluster to a sticky piston and connecting it to a redstone clock I was able to harvest 3,004 shards in 5 minutes. This only works if the cluster is placed on the piston so that the base is on the sticky part, and it does not work with non-sticky pistons, as the crystal breaks when the piston is retracted, and it does not work with buds, although the breaking particle effects do appear

I have attached screenshots of the setup I used and of the chest that all of the shards were sent to