Sounds like the prosecution forgot to tick the "charges dismissed without prejudice" box on the agreement form. But maybe not.
I've been watching a lot of court proceedings lately. It turns out a lot of jurisdictions have a "charges dismissed on completion of probation" type judgement option. Basically the defendant agrees they committed the crime, and gets sentenced, but the conviction is deferred until the defendant completes probation. If the defendant is successful on probation, the conviction is waived, and it's like they never committed the crime at all. Exact details and extent of the amnesty vary from jurisdiction.
If that's what Smollet agreed to, then yeah, he absolutely should not have been prosecuted again. So much so that it boggles the mind that the second prosecution would ever have gone through to sentencing. The presiding judge should have thrown it out on a pretrial motion from the defense.
Which makes me think that there was something fishy about the original bargain with the prosecutors. Most likely that the dismissal was not conditioned on admission of guilt - essentially an out of court settlement more like arbitration than an instance of jeopardy before the law.