You seem to have mistaken active “plea bargaining” with finished and accepted “plea deal” which is ALWAYS finalized by the judge. Without the judge, there is no acceptance.

There is a hearing, the judge is presented with a plea deal, both sides as well as the defendant are directly quizzed in regard to the content of the plea, its conditions and whatever the defendant has sworn to provide, and as a part of that the judge can accept, reject, or ask the two sides to work on it further.

In practice, this means that whatever amendments the judge wants as a condition for accepting the plea, the judge gets, OR the plea in its present form is scrapped and prosecution proceeds or the two sides go back to the bargaining table.

Read your quotes again. They literally do not say anything different than I just described.