The winner of an open 2024 Democratic primary for the presidential nominee would be the same as the last two open primaries the party has held: Whoever gains the blessing of the Big O himself.
While Obama could have handed anyone the nomination in both 2016 and 2020 with his endorsment, he didn't
Hillary Clinton and Joe Biden won the nomination without the help of Obama.
(Obama calling Klobuchar and Buttigieg to drop out probably did speed things up for Biden, but only by a week?)
Both HRC and Biden won the nom in part to having the support of the Democratic establishment, which from what my little brother has told me from working on Casey's, Maxwell's, and Biden's campaign worships the ground Obama walks on. His approval of a candidate is not an indicator for success, but his disapproval would be a death knell.
Thing is Warren's still in his good graces from being his head of CFPB so who knows?