Here’s my GUESS below:
If a president were found to have been ineligible for the office, then he is automatically NOT president. It wouldn’t be a matter of impeaching him.
I think it would be a matter of the vice president simply taking over. I believe the current reading on succession says that ANYTHING that incapacitates the president results in the elevation of the VP until the incapacity is removed. Ineligibility could not be removed.
Also, the TEAM of Biden and Obama ran, so all of those winning votes were also his.
Imho, this would require the involvement of the courts, and at the level of legal interpretation and not at the level of the chief justice being presiding judge over an impeachment.
A strict reading of the Constitutional language does mean Biden already is acting President, doesn't it?
Would that explain a few of ol' Plugs' weird Al Haig moments in the foreign policy arena, lol?
Remember, if Joe Biden takes over and something happens, Nancy Pelosi is just a heart beat away.