Why is the texture of the pasta in a store-bought pasta salad different to the texture of pasta I've cooked at home?
Expanded from the comments...

Use properly salted water when cooking the pasta.

Slightly undercook the pasta a little bit; the pasta will continue to cook as you prepare the salad.

Do not rinse the pasta.

Mix the ingredients while the pasta are hot; they will absorb more flavour; I would try to season the pasta before adding oil; since oil will tend to coat the pasta and will block the seasoning from being absorbed.

Use a little bit more salt and spices than usual (cold dishes need more "punch".

Good luck and have fun experimenting.