It has never been elaborated on exactly what that eye was made of, and whether it has additional features, e.g. stimulating cell regrowth (cells which are in and of themselves Asgardian).
It's also unclear whether Thor's All-Father strength is physically applied to his biological material, or rather applied to his body in general. Because if you assume that it's only applied to Thor's biological material, are you then also expecting the clothes he wears (or even the food in his stomach) to be disintegrated as well?
There's no real information on this eye, nor on Thor's All-Father strength, to draw any real conclusion here.
In my opinion, Thor enduring the focused energy of a star is insanely out of scope of any real-world consideration. Any being able to withstand that would be ridiculously unstoppable, even more so than Thor is already represented in the MCU. Thor can get wounded from combat, and no opponent we've seen Thor battle is going to come close to matching the focused energy coming from a star.