Saw this play recently as a spectator, not sure what the right answer is...
13U league, dropped 3rd strike rule in effect. One out, runner at 3rd, count was 0 and 1.
Batter swings wildly at a pitch, catcher drops the ball (right in front of themself). First base coach starts screaming for batter to run to first, that the catcher dropped a third strike. Batter takes off toward first, catcher sees this and throws the ball down to 1st. Runner is "out" at 1st but runner on 3rd comes home to score as a stolen base. In the mayhem, Umpire's hands are up yelling for the batter to come back, that was not the third strike.
First base coach says whoops, I lost track of the count. Batter is allowed to return to the box and finish their at-bat. But run counts as the steal.
Would the batter be 'out' for running to first? Or should the play have been deemed dead and the runner asked to return to 3rd? Or did everything work out correctly according to the rules?