Ah, so it looks like maybe you multiplied instead of using exponential. Problems with Reddit formulas lol. So it’s Teff^4 or to the power of 4 vs times or multipled by 4.
Here’s a nice widget that you can play around with to get different amounts. Astronomers use widgets, you may as well too lol. Gigawhatts are 10^9 more than a normal Whatt, you can use Google converter for help there as well. I’m getting ~667 degrees C for your star.
I’ll caution you that a baseball sized star will have a weird composition, if it had a d’impair makeup to our sun the gravity and gas pressure would be not be in balance at that size and the star would expand rapidly until fusion stoped, as which point it would likely be too spread out to collapse back in. The smallest physically possible stars( with how we understand physic today!) are neutrino stars, and they are tiny for stars, which means they are about 6 miles or 10 km in diameter.
Using this rocket equation calculator:
If you have an exhaust velocity of 50 km/s (reasonable for an ion thruster), and if your fuel makes up 99% of the entire weight of your spaceship (difficult but not unimaginable) then your maximum speed will be 230 km/second.
If you can pump more energy into your ions to speed them up even more you will get better results. According to the same rocket equation calculator, if your exhaust velocity is 99% the speed of light, and your mass fraction unchanged, your final velocity will be about 4 times the speed of light. So clearly this calculator can't handle relativistic effects.
Given that we know very little about your location, the direction you are viewing the star at, its apparent magnitude, and other critical things, I suggest you download an app such as Sky Map (Android) or Star Chart (iOS), which allows you to point your smart phone or tablet at the sky with an overlay on your phone/tablet telling you what you're looking at :)