This is more a testament to how large the Oort Cloud is since the sun is pretty average. Sirius is 25x the brightness of our sun, but the edge of the Oort Cloud is 200,000x farther from the sun than Earth is (Pluto and the Kaiper Belt are only 40x and 50x). If Earth was at the edge of the cloud, Sirius would be only 3x farther then the sun; so at 25x brighter it would be brighter. But within a 20 ly distance our sun is one of the brightest, and of the 130 closest stars our sun is actually the 7th brightest.

The Oort Cloud reaches out 3 ly, and for comparison our closest neighboring system, Alpha Centauri, is 4.3 ly. If you were at the edge of the Oort Cloud, our sun would be the 5th closest star to you.