The laws and constitution are quite explicit on the issue of VP and President
If you are barred from serving more than two terms , you are constitutionally barred to be VP
Technically, nothing in the Constitution prevents anyone from serving more than two terms. The 22nd Amendment prevents someone from being elected to more than 2 terms. That is the rub here. Now logic would seem to dictate that if you can't be elected as president you can't be elected as vice president, but there is nothing specifically in the Constitution about that. The 12th Amendment says if you are not constitutionally eligible to be president, you cannot be vice-president. The Constitution only has 3 eligibility requirements for president - over 35, natural born citizen, a resident of the US for the past 14 years.
The argument they will raise is that Obama obviously meets the constitutional eligibility requirements since he has already served as president before. They will argue that he could not be elected president, but if elected VP he could serve as president because he was not elected as president more than twice.
Keep in mind that we have already have had at least one president that was not elected as either president or vice-president. Gerald Ford was a congressman from Michigan when Spiro Agnew resigned. He was appointed as VP by Nixon and approved by Congress. Then Nixon resigned and Ford became president. So you could even see a scenario where Biden and some other person as VP (Harris would never go along with this) were elected. After being sworn in, the VP could resign and Biden could appoint Obama as VP. If the Dems had a majority in both houses of Congress, they could approve the appointment. Then Biden could resign and Obama would become president.
If SCOTUS decided this was a political question and refused to decide it, what could anyone do to stop it? And I can think of at least 4 votes on SCOTUS that would be happy to punt on an issue like this - the three libs and Roberts, Roberts because he wouldn't want SCOTUS to be seen as deciding the election. All they would need would be one more - Kavanaugh or ACB would both be good candidates. Remember, SCOTUS refused to get involved in any of the election cases in 2020.