As of a few hours ago, Novak was still in visa limbo at the airport:
https://www.cnn.com/2022/01/05/tennis/australia-djokovic-exemption-backlash-spt-intl-hnk/index.html
According to this and a few reports I heard, the federal government and the state of Victoria and tossing it back and forth like a hot potato, as no one seems to want to be responsible for stepping into what is already a politically perilous situation. Apparently, the visa that Novak's team applied for doesn't allow medical exemptions from vaccination, so that's trying to get straightened out. According to this article, citing local Australian news sources, it probably will get straightened out, and he will go to Melbourne and play.
In retrospect, Djokovic might be sorry that he put up his cheery tweet that he had his exemption and was on his way to Australia, since, by the time he landed, the news had already raised a huge controversy. It might have all gotten settled more easily. As it was, however, he'd already become every politician's nightmare by the time he'd arrived.