A lot of that is not correct.
There is abundant Supreme Court authority for the proposition that when a person who is not eligible to hold a position is de facto installed, they do not legally hold the office and their acts are void.
So those acts which take a "president" to make effective are of no force. The two Supreme Court appointments are two good examples; there are others.
But that does not vitiate everything that has happened in his period either.
Absent intervening adjournments or other interruptions, Congress passes a bill; the President has ten days in which to sign it into law; or veto it. If the President does not act in the ten days, the bill becomes law.
So if you view legislation which was passed which he executed as simply without execution because his execution was void; the ten days passes; it would seem to me that the Court would hold the legislation became effective without the signature of the sitting President or action by a sitting President to Veto it.
On the other hand, as we know, if Congress adjourns after the bill is passed but without signature or veto, the Constitution provides that the bill is "pocket vetoed". So if there was legislation in that category, it would not have become law.
Under Section 3 of the 20th Amendment, the Constitution addresses the current situation specifically. When the election of an eligible person as Vice President is certified but no eligible person is certified as President, the Vice President becomes acting President. Since January 2008, Biden has been Acting President.
I believe that some Presidential power has, at the insistence of Mrs. Clinton and Panetta, been exercised jointly or otherwise by Biden.
So a fair amount of action has been taken that stands up as effective.
Obamacare? I am not certain as to the timing of passage and adjournment. I now am inclined to believe that Congress did not adjourn until ten days had passed and thus that Obamacare became law but I have not studied the record sufficiently to render an opinion.
I am not familiar with that "abundant Supreme Court authority." Could you post the citations?
Here are the US Supreme Court precedent rulings:
“The de facto officer doctrine confers validity upon acts performed by a person acting under the color of official title even though it is later discovered that the legality of that person’s appointment or election to office is deficient.” Norton v. Shelby County, 118 U.S. 425, 440 (1886).
“The de facto doctrine springs from the fear of the chaos that would result from multiple and repetitious suits challenging every action taken by every official whose claim to office could be open to question, and seeks to protect the public by insuring the orderly functioning of the government despite technical defects in title to office.” 63A Am. Jur. 2d, Public Officers and Employees § 578, pp. 1080-1081 (1984).”
The new president (Biden) could simply pardon the outgoing president and then it would just be a simple case of presidential succession via the 25th Amendment.