We know definitively what the biggest solar system in our galaxy is. It’s ours! Our sun and planets.
Because it is the only one called the “solar system”, since “solar” comes from the word “sol” or “sun”. So it’s literally the system of bodies around the sun.
But when we correct that to “star system”, we really have no idea what the largest one is. As strange as it sounds, we know orders of magnitude more galaxies than star systems. So the odds are overwhelming we have not found the largest star system in the galaxy.
However, all jokes aside, it is possible that our own solar system may be up there. The largest star system we have found to date is Kepler-90, with 8 known planets. That happens to be the same number of planets in our solar system. However, smaller planets are difficult to find in other star systems so Kepler-90 very well could have more hiding in there.