It can be confusing, but just because you see the field in the database does not mean the field is registered when you are trying to update it. I don’t know the entire sequence of events that are fired when you use the draft_to_publish hook or what files may or may not be loaded at the time.
But that really did not answer my question. Are the fields registered in a function? Is this function run on a hook? Are are the calls to the ACF function just at the top level of the file outside of any functions?
As a test to see if the field is registered, if you want to do some debugging, just before you try to call update_field() for this update you can try getting the field object.
$field = get_field_object('field_YOUR-FIELD-KEY');
var_dump($field);
