As it stands, Joe Biden has not been elected to anything and can only be the president-elect once the Electoral College votes for him on December 14. Until then, he is the potential President-elect and nothing more.
The Electoral College vote can only happen if Trump concedes or all the legal challenges asserting that the election was stolen fail. As Trump won't concede until all legal and constitutional options are tried and tested, the future of the Republic rests in the hands of judges.