I used to keep it on the short stick to reduce sound, but read that may contribute to warping, so now it’s always on the long stick.
If short stick may contribute to warping, why wouldn't full stick do the same?
It has to do with physics. There is much less gravitational pull/stress on the lid when on the tall stick/prop. Take a piece of 4'X8' plywood and prop it up at a 45*/50* angle and notice the bow/warpage of the plywood. Next, prop up the sheet of plywood at a smaller angle, say 20*/25* and notice the warpage/bow.
I know the lid of a grand piano is thicker than a sheet of plywood, usually, (depending on the plywood) but the principle is the same.
I've seen noticeable lid warpage on grand pianos whose lid is left propped on the short stick for long periods of time. I'm sure there could be some warpage on the piano lid left propped on the tall stick/prop for long periods of time, but short stick/prop will lead to lid warpage much faster.
Also, the material the lid is made of can affect warpage to an extent, but the results will still be the same over a period of time. A good quality lid material will likely warp much slower over time. Cheaper, heavier (MDF) lids will warp faster.
Removing the lid prop and closing the lid when not playing will help prevent warpage, whether on the tall prop or short prop.
Just my .02.