Jean Philippe Aumasson[1] is an important currently active cryptographer who studied this particular problem closely. If he says he does not expect an algorithmic break of SHA2, I believe him that I don't need to plan to switch from SHA2 to SHA3 in an hurry.

I don't have the math to understand a more detailed explanation for his reasons to make such a statement. If you do have the math, ask him.

1 - https://131002.net/index.html