It turns out that the Sun is pretty close to perfectly round. There was some thought that it would have a slight bulge near the equator because it is spinning (like Jupiter does). But, a careful study done in 2012 using data from the Solar Dynamics Observatory (SDO) showed that any bulge was very, very small.

No the Sun is like a squat circle. Like if you sat on a beach ball and it squished out at the sides. We call this an oblate sphere. The oblateness on the Sun is very tiny though, it's almost a perfect circle. The difference in the top to bottom distance compared to the side to side distance is about 0.001%, so miniscule. Scientists had to measure very carefully to be able to make those measurements. You can read about them here: https://science.nasa.gov/...2008/02oct_oblatesun