In 2000, Gore did not reconcede nor did Clinton release transition funds until after the Supreme Court ended the dispute. Neither Bush nor Gore was out there acting as President in that time either.
Had to show this to the wife a few nights ago: Gore never really conceded; after the USSC ruled against him, he said he’d accept the electoral college results. The availability of challenge opportunities for him was over and done; there was nothing further he could do. He was cooked. The USSC ruled: no equal protection violations. He didn’t challenge any other states legally; the statutory timeframes had run out for challenges at that point, time was up.
He never conceded and acknowledged defeat to Bush.