yes, the Newtonian center of the solar system is demonstrably a point precessing around the center of the sun mass.
but the sun is so massive, that precessing point is far less than its radius away from the center of the sun.
Jupiter makes up the bulk of the itty rotational centerpoint shift
Newton's orbital equations describe macroscale behavior very, very well. other galaxies and the dark ebwrgy/matter craziness?my guess is there a red a few things making our observations sus, a few more things and energies we haven't a clue about yet, and potentially some very weird compounding effects of supermassive/superenergetic objects and/or conglomerates.