That’s mostly correct.
However I thought the judge in Hunter’s case rejected the plea deal, not Hunter.
No, the judge asked probing questions about the plea deal, and got the prosecution to admit that Hunter was still under investigation and that the plea deal would not cover any potential FARA indictment, so Hunter's lawyer said the deal was off.
Hunter entered a plea of not guilty, then the judge gave the parties 30 days to renegotiate the plea deals.
This ain't over yet. They will meet again in court in 30 days and try the plea deal again in front of the judge.