Why the more-luminous star has larger surface area when two stars have the same temperature?
I'd say your problem is that you are imagining the light rays emanating out from the center of the star.  Try it again with light emanating from each square area on the surface, and you will see that being at the same temperature means each square on the surface sends out the same number of rays, but there are just more such squares.  Then you will see a lot more light rays coming from the larger star, in proportion to its surface area.