I think whoever writes it. At any rate, I expect it to be released on the last day.
You are in the ball park, but it isn’t that exact.
The votes of the justices at conference are not final. The draft opinions are not final. The entire process is much more amorphous than what goes on in a Senate or House cloakroom.
At conference, the judges vote on the case. The senior justice in the majority assigns the opinion. That Justice gets a first shot at creating a draft.
That draft is circulated amongst the other Justices. What the author of the opinion wants, is a written note back that says the other Justices who have read the opinion join it. In many cases, that isn’t always immediately forthcoming. They may respond with something like “I will wait on the dissents and concurrences” they may respond with “Change this, this and this and I can join.”
The opinions are written, rewritten and rewritten again as the Justices negotiate amongst themselves. Sometimes, during the process, a Justice switches their vote, and what was going to be a majority becomes a dissent or a concurrence.
The opinions (and votes) are not final until the opinion is released for publication. Then and only then is it posted on the Court’s webpage and recorded in the Reporter. That only happens when the majority opinion AND all dissents and concurrences are finished.
There is a final deadline (the last opinion day), but everything is pretty much open until then. What is most likely going on right now is waiting for a dissent (or multiple dissents) to be finished.
The majority author will often address the dissenting Justices in the majority opinion. Notice that this is missing from the Dobbs draft.
I can GUARANTEE you that it will probably have changed from what Politico posted. How much remains to be seen.
In all of this, the Chief ... Justice ... Does ... NOT ... CONTROL ... WHEN ... OPINIONS ... ARE ... RELEASED.
Dumbs, like the brain-dead “journalist” who wrote this “article” need to quite opining on things that they don’t understand.