Trump's attorney, Sauer, under questioning by Justice Amy Coney Barrett, conceded that the core allegations are private acts, not presidential acts.

But not all of them. And because the lower courts didn't conduct an assessment of the individual acts, the case isn't presented in a way that puts his specific acts before the Court. The lower courts just ruled - categorically - that there is never any immunity against criminal prosecution for an ex-President, regardless of whether the acts were official or private. Since that's the question before the Court, they can either agree with that or provide a different rule that says that some "bucket" of actions are immune and others aren't - and presumably some guidance on how lower courts are to decide whether a specific act falls into which category.

It doesn't sound like the members of the Court were on the same page on what that different rule might look like, so it might take some time for them to hash that out. It does sound like there's a majority that believes that some Presidential official acts might be immune from subsequent prosecution (just like all his official acts are immune from civil suit). That would almost certainly result in the case being sent back to the lower court to conduct further proceedings to determine which (or any) of the actions that underlay the charges were immune and which were not.

So, this almost certainly will result in a months-long SCOTUS delay, and probably several more months of pre-trial proceedings on the immunity issue before the case moves on. If the Court rules that immunity is available for some Presidential actions, I think it's almost a certainty that this case doesn't get to trial before November.