Unfortunately, Jefferson himself fell afoul of that with the Louisiana Purchase.

That's not true, in fact, this is exactly what he wanted, and I've been trying to tell people this is 100% the correct course for years.

The Federalists tried pulling all the same shit that the Democrats did because they were anti-Liberal, government first, authoritarian freaks. It's why Hamilton got a musical.

The Alien & Sedition Acts were passed to, theoretically, protect the country from illegal migration; but it instead was used to crush political dissent by banning criticism. Hundreds of people were imprisoned, in direct violation of the 1st Amendment, for insulting the president, congress, and the Federalists. Including shutting down whole newspapers. Jefferson ran his campaign on mass pardons for everyone who were rounded up and arrested, including his own supporters. He did not appeal to court rulings because a) SCOTUS did not have the right to overturn congressional law; b) it was the responsibility of the executive not to enforce illegal and unconstitutional laws. When he won, and the Democratic-Republicans won both houses of congress, they immediately re-wrote the Alien & Sedition Acts, and Jefferson pardoned everyone. That should remind you a lot of what Trump did with the J6'ers because it's the same thing.

Your mentality is actually one of the reasons why all this happened in the first place. These acts were passed under John Adams who explicitly stated that even though the thought the laws may have been unconstitutional, he didn't believe it was the right of the executive to veto laws passed by both houses of congress. "Well it was Democratically done, and the president shouldn't have this power!" is provably wrong, no matter how much I like Adams.

As for clearing the Deep State, this is exactly what Jefferson tried to do again. In Marbury v. Madison; Madison was Jefferson's cabinet pick, but Marbury was Adams' cabinet pick. Marbury claimed he couldn't be removed from office because his term was for 4 years. Madison sued and the case went straight to SCOTUS because it's basically original jurisdiction and I don't think there were other federal courts or federal appellate courts.

Unfortunately, this is where SCOTUS gave itself the power to overturn law at the discretion of 4 justices (there were 7 total at the time). They did not have that power before. The original intent was for Jefferson to do what he did. SCOTUS did correctly point out that the cabinet and executive branch appointees only exist at the pleasure of the President, so go fuck yourself Marbury. This is what allowed Jefferson to purge the executive branch of Federalists, preventing any further enforcement of illegal laws, while the Democratic-Republican congress finished the job in the Legislative branch. He decided not to argue SCOTUS's point because now law had actually been overturned, and the immediate threat was the Federalists not the Judiciary.

Trump isn't going against Jefferson, he's fucking replicating his efforts.