Williams v Pennsylvania, "officer of the court" status and invalidation of ALL criminal convictions in the United States

In 2016, the U.S. Supreme Court, through Williams v Pennsylvania, said that a judge cannot be at the same time an "accuser" and an "adjudicator".

So, judge and prosecutor cannot be ONE.

In other words, judge cannot be prosecutor, and prosecutor cannot be judge (part of adjudicating court).

But, every prosecutor is a sworn "officer of the court".

And, attorney disciplinary prosecutors are also deemed an "arm of the court" - see the saga of how I sought a FOIL request from such a disciplinary prosecutor who kept claiming she was part of the court, here and here.

So, if a judge is the court, and the prosecutor is the court (officer of the court), the judge = prosecutor, and prosecutor = judge in EVERY criminal case.

Now, every criminal case in the United States, due to this "officer of the court" requirement for all prosecutors, has been invalidated by Williams v Pennsylvania, including the death penalty cases which are scheduled for execution?  Including those where people were already executed?