And why would being convicted of that crime disqualify him from running for president again? There are various cases here: he could have been quickly impeached in the House and convicted in the Senate before Jan 20 (that would disqualify him); convicted by the DOJ after Jan 20, but before the primaries; during the primaries; after becoming the GOP nominee; convicted in a state court and disqualified under the 14th. In that last case, assuming Trump appealed it, why would SCOTUS be more likely to rule that Trump is disqualified everywhere? Shouldn't the "voters decide" regardless? They didn't discuss the definition of insurrection much at all during the recent appeal hearing.

Someone who has engaged in insurrection while an officer of the United States is disqualified from holding office. If we assume (arguendo) that this applies to the Presidency, it seems clear that someone who has been tried and convicted for the federal crime of insurrection would have been sufficiently proven to have met the standard for that disqualification. So if Trump had engaged in activities that led to his trial and conviction of that crime, that would be a set of circumstances where he would be disqualified. Hence, my answer to your original question.

Part of the reason that nearly every Justice was skeptical of a state-by-state determination is because that's not what happened with Trump. Trump wasn't "convicted" in a state court. There was a collateral finding in a civil proceeding in a lawsuit between voters and the CO secretary of state. That type of proceeding, unlike a federal criminal trial, allows a lot of variation and "wiggle room" for different states to reach different conclusions. States can differ on the standard of review, their own interpretations of what constitutes "engaging" in an "insurrection," their evidentiary rules, the actual evidentiary record, etc.

The reason they didn't get into the definition of insurrection much at the appeal hearing is because it is exceptionally unlikely that the SCOTUS' decision will turn on whether Trump did or did not engage in insurrection. Rather, it's more likely to turn on questions of who makes that determination: states, Congress, federal courts, or the voters.