That clinches it, this star is about 45% more massive than it should be, given its circumference and luminosity.
My guess is that the extra mass has been bound up in a toroidal singularity. That would allow the wormgate to shunt mass into and out of the star as required.
Toroidal singularities are unstable, though. There would have to be some exterior systems keeping it from vomiting all of its mass at once.
With the sphere infrastructure destroyed, that theory should be easy enough to prove.
Echo-map the star?
No. Just wait for it to explode.