The 19th century was a time of letter-writing, not Signal group chats. For that reason, I think that if the governor of Georgia had explicitly asked Jackson for permission to defy the Supreme Court, we would probably have a copy of that letter or at least a mention of its existence in the correspondence or journals of these men or of their secretaries. I also don't think Jackson was so brazen as to give a go-ahead to defy the Supreme Court. Such an action would have undoubted started a major incident if the press found out about it, and may have even caused the unravelling of the federal system, and Jackson was certainly no idiot and knew this.
With respect to the current situation, I think the current president and attorney-general are more or less just as willing to disobey the courts. Georgia officials in the Cherokee incident(s) only did so because they were politically accountable only to the white, landowning, citizens of Georgia, who were behind them every step of the way. In a similar vein, the voters seem to have delivered a message to Trump in 2024 that there is no political cost to authoritarianism and disrespect for the rule of law. Or, at least, that's the message Trump thinks the voters sent him. In reality, such a cost does exist, and it's why Trump lost in 2020. Though Allan Lichtman's prediction of the 2024 presidential election outcome was definitely wrong, I still think that his overall message, that voters care more about whether the incumbent president is good or bad than whether their opponent is good or bad, makes a lot of sense to me. But I'm no expert in that.