They still have no Constitutional power to override the president when he exercises his Constitutional powers. If they did, the president would be neutered. That was not the intention of the Framers. Besides, no Republican signed the attempt to thwart the president.
But this is about whether they can get bureaucrats to continue to stonewall and redact document requests as has been the case with Congress’s document requests for months. Everyone does not agree that the president has such power and it could end up in court if bureaucrats defy the president.