Congress, I believe, would not have the authority to say Asylum from What as it appears they have granted that authority to the Executive.
They could change the statute. But it would not affect those granted the status prior to the change in statute. So, it would be the same affect as granting permanent residency.
What I’m saying is that the opening paragraphs of the law will define to whom it applies. When all is said and done those words have not changed and a follow-on president could reverse direction and actually enforce the law as intended.