Treating the sun's surface as a static blackbody radiating surface, it's straightforward to calculate gravitational redshift. However, a search and it turns out there are significant contributions from convective motions that have to be factored in. Here is the article setting out all the significant contributions: https://arxiv.org/abs/1207.0177Do we observe any significant shift (red or blue) once it leaves the surface?
That finally received on Earth's surface will have a slight added gravitational blueshift component as a result (only the difference in gravitational potentials counts), but will far below the solar redshift contribution.