This is damned close to a Bill of Attainder seeking the political death of President Trump. Think of it, the Legislature attempting to declare one person and only one person ineligible to run for President in the future. ISN’T THAT UP TO THE VOTERS TO DECIDE???
I agree that they might just try to impeach after he has left office, but I doubt the Senate will agree. What probably will happen is a bill to disqualify him from being able to run. I’m not sure how they will word it so that it is not a bill of attainer but they will find a way to do it. Congress can set election laws by a simple majority vote.