`replaceChild` method in BinaryTreeNode is not correct

Missing update parent. It should be

    if (!nodeToReplace || !replacementNode) {
      return false;
    }

    if (this.left && this.left === nodeToReplace) {
      this.left = replacementNode;
      replacementNode.parent = this;
      return true;
    }

    if (this.right && this.right === nodeToReplace) {
      this.right = replacementNode;
      replacementNode.parent = this;
      return true;
    }

    return false;
  }

Start at the BinaryTreeNode.replaceChild method and inspect how its left and right child links are used. Confirm that a successful replacement also updates the replacement node's parent reference, then run the relevant BinaryTreeNode tests if available and verify both child positions and failure cases.