So first things first, a short crust pie dough is usually made with cold butter and ice water. This leads to a flakier, more tender dough. You also typically don't want to knead the dough. Too much gluten development leads to a tough, chewy crust.
A more typical shortcrust would start with cold butter cut into cubes. Put the flour, salt, and butter in a food processor and pulse just until it looks like wet slightly clumpy sand (there should still be intact bits of butter in the dough). If you don't have a food processor, you can either use pastry cutters or a couple of forks to cut the butter and flour together or my favourite method: freeze the butter and grate it before rubbing it into the flour with my hands. Slowly add ice water until the dough can be shaped into a rough, shaggy ball. It should not look smooth at this point. Cover and let it rest in the fridge for at least an hour.
Then you take the rough, not smooth looking ball of dough and roll it out on a floured surface. The first time you roll it out, it will be very crumbly. Just roll it out as well as you can. Then you can fold in the rough edges and roll it out again. Repeat as needed. I typically need to do two or three fold+roll iterations before I have a smooth, easily workable pie dough. Folding and rolling will get you a smooth dough without as much gluten development as if you kneaded it smooth and you will keep the little bits of butter that give you flakiness when the pie bakes.
There are of course endless variations on shortcrust pie dough recipes. There are people who swear by using lard or vegetable based butter substitutes, use vodka instead of water, or add different flavourings to the dough. But the basic method for shortcrust is cold fat + cold liquid + minimal handling. And industrial recipes add various preservatives and chemicals to force certain reactions that are hard to get hold of as a home cook. However, you can still make very good pie dough at home without those additives.