All the solar system matter contributes to an object’s orbital center but that’s constantly moving as the system moves.

I think (?) most planets have their barycenter inside the sun’s surface

The gravitational pull of system matter pales in comparison to the sun so you don’t need to consider it unless you’re navigating satellites.

You can try KSP (Vanilla) versus Kopernicus mod if you want to feel the difference.

Also called n-body