Following the documentation sample, I\'m trying to create a function that searchs for a numerated list in a google document and, if finds it, adds a new item to that list. But I
Following my comment, I tried to play with your script to see what happened and I came up with that code below...
I'm not saying it solves your issue and/or is the best way to achieve what you want but at least it gives a result that works as expected.
Please consider it as a "new playground" and keep experimenting on it to make it better ;-)
function test() {
  var elementContent = "New item testing"; // a paragraph with its formating
  var targetDocId = DocumentApp.getActiveDocument().getId();  
  var targetDoc = DocumentApp.openById(targetDocId);
  var body = targetDoc.getBody();
  var childIndex = 0;
  for (var i = 0; i < targetDoc.getNumChildren(); i++) {
    var child = targetDoc.getChild(i);
    if (child.getType() == DocumentApp.ElementType.LIST_ITEM){
      while(child.getType() == DocumentApp.ElementType.LIST_ITEM){
        child = targetDoc.getChild(i)
        childIndex = body.getChildIndex(child);
        Logger.log(childIndex)
        i++
      }
      child = targetDoc.getChild(i-2)
      var listId = child.getListId();
      Logger.log(childIndex)
      var newElement = child.getParent().insertListItem(childIndex, elementContent);
      newElement.setListId(child);
      break;
    }
  }
}
