You’re not wrong. Everything orbits the center of mass of the system, meaning the mass of the star and the body in orbit. And that is handy for astronomers, many exoplanets have been found using the Doppler spectroscopy method. Doppler spectroscopy measures the Doppler shift in the star’s light as it is pulled towards and away from us by planets in orbit. The newest spectrographs are sensitive enough to detect a star’s wobble caused by an Earth sized body in orbit. The barycenter is still within the star, but not at the center of the star’s mass.