While I'm not a "constitutional lawyer," I don't think one is required to be one in order to address the question in the first instance. The starting point, it seems to me, would be Amendment XX of the U.S. Constitution, which provides, in pertinent part, as follows:
Section 1.
The terms of the President and Vice President shall end at noon on the 20th day of January, and the terms of Senators and Representatives at noon on the 3d day of January, of the years in which such terms would have ended if this article had not been ratified; and the terms of their successors shall then begin.
Per Section 1, the current terms of Biden and Harris will end automatically at noon on January 20, 2025. There is no constitutional scenario in which Biden or Harris would "continue in office" or "remain in office" or anything like that. Biden and Harris would either be elected to a second term or they would not be.
Section 3
If, at the time fixed for the beginning of the term of the President, the President elect shall have died, the Vice President elect shall become President. If a President shall not have been chosen before the time fixed for the beginning of his term, or if the President elect shall have failed to qualify, then the Vice President elect shall act as President until a President shall have qualified; and the Congress may by law provide for the case wherein neither a President elect nor a Vice President elect shall have qualified, declaring who shall then act as President, or the manner in which one who is to act shall be selected, and such person shall act accordingly until a President or Vice President shall have qualified.
Seems to me that, in the situation where Trump were to receive the required 270+ Electoral Votes but is somehow subsequently "disqualified" by Congress, then Trump's running mate -- who presumably also separately received 270+ Electoral Votes -- would become the acting President.