在TypeScript中扩展重载方法时出现问题

In a parent class, I define a method with different parameters: an index in a store or an element, and depending on the parameter, I get the element from the store by its index or just use the given element.
Thus, I use overloading to define these methods:

class Parent<T> {
  items: T[] = [];
  item: T = {} as T;

  applyMethod(index: number): void;
  applyMethod(item: T): void;
  applyMethod(param: number | T): void {
    if (typeof param === 'number') {
      param = this.items[param];
    }
    this.item = param;
  }
}

class Child1<T> extends Parent<T> {
  // In my application, I actually add an id: string overload.
  override applyMethod(param: number | T): void {
    // Do something more before calling:
    super.applyMethod(param);
  }
}

class Child2<T> extends Parent<T> {
  override applyMethod(param: number | T): void {
    if (typeof param === 'number') {
      super.applyMethod(param);
    } else {
      super.applyMethod(param);
    }
  }
}

在TS Playground强中也能看到它.

在Child1中，我有一个错误:

No overload matches this call.\
  Overload 1 of 2, '(index: number): void', gave the following error.\
    Argument of type 'number | T' is not assignable to parameter of type 'number'.\
      Type 'T' is not assignable to type 'number'.
  Overload 2 of 2, '(item: T): void', gave the following error.\
    Argument of type 'number | T' is not assignable to parameter of type 'T'.\
      'T' could be instantiated with an arbitrary type which could be unrelated to 'number | T'.(2769

我可以像《子元素2》中所展示的那样解决这个问题，但它非常奇怪/愚蠢.

另一种解决办法是定义applyMethod(param: any): void {}，而不是number | T.它是classic 的，这就是我最初所做的，但我发现TS只看到param: any参数定义，因此我输掉了输入.

我 Select 了另一种方式，拨打了super.applyMethod(param as any);.至少，输入保留了它们的类型.

有没有其他更优雅的方式？我错过了什么吗？