My understanding:
- The reason the SEC didn't support an evidentiary hearing is because all their theories rely on undisputed evidence.
- I am very certain that Elon's team will ask for an evidentiary hearing, becase it's the only way to get the following pieces of evidence admitted:
- The expert opinion and expert testimony Elon's first reply relied on in part. The SEC would want it either excluded as inadmissible, or have it at least cross-examined. They might also want to submit their own expert opinion.
- The lawyers negotiating the settlement could issue affidavits and be subject to cross-examination. This establishes a chain of evidence regarding "intent". Both settlement contract intent and Elon's intent when he was writing the tweets matters.
- Elon's team might want to call hostile witnesses from the other side, to cross-examine them against email evidence and other testimonies.
- Various email chains might not be undisputed, because incomplete or lacking other context such as attachments.
- If Elon's team wants to play hardball they could ask for limited discovery to support their theories. (I don't think they will, the interesting bits will be under attorney client privilege.)
- A contempt hearing typically only takes testimony from the defendant. This is good for the SEC but not enough for Elon's team.
All these pieces of evidence would be appeal-proof if properly handled, and the evidentiary hearing would allow them to be catalogued and recognized by the court, or at least a proper mechanism would be established to get them admitted.
Note that contempt of court hearings have very little procedural framework that I could find - they are free-form to a large degree, with a lot of discretion given to the judge. I have no idea what she wants this to become - and asking the parties gives her a first approximation about how much evidence there is to handle.
My (tentative) guess: there's probably going to be an evidentiary hearing, before a contempt hearing is held. The judge would want all evidentiary disputes resolved by the time she is asking questions from Elon.