你没有从你的函数中返回任何东西，这是使用异步代码时的一个基本错误。
只需使用async/await作为axios响应，itemsChildren也应该是async

computed: {
  async itemsChildren() {
    if (this.parentReview == null) {
      return null;
    } else {
      const formData = new FormData();
      formData.append('ID', this.parentReview["ID"]);

      try {
        const response = await axios({
          method: 'POST',
          url: window.location.origin + '/API/List',
          data: formData,
          headers: {
            'Content-Type': 'multipart/form-data',
            "RequestVerificationToken": document.forms[0].querySelector('input[name="__RequestVerificationToken"]').value,
          }
        });
        return response.data;
      } catch (error) {
        if (error.response.status == 401 || error.response.status == 402 || error.response.status == 403) {
          window.location.href = error.response.headers.expiredtokenredirecturi;
        }
        console.log(error.response);
      }
    }
  }
}

PS：我想帮忙，但我不知道computed是什么，它是如何工作的，甚至异步是否可以与它一起使用。
你可以在这里阅读异步编程：https://dev.to/raxraj/asynchronous-javascript-from-callbacks-to-asyncawait-a-journey-through-evolution-5578

您没有正确返回您的axios请求。您可以返回axios请求，或者更好地执行以下操作之一。我也不认为来自服务器的401，402，403响应会触发错误。但是你应该验证这一点，因为我不确定axios如何处理那些响应。

使用Promises

computed: {
    itemsChildren() {
        return new Promise( resolve => {
            if ( this.parentReview == null ) return resolve(null);

            const formData = new FormData();

            formData.append('ID', this.parentReview["ID"]);

            axios({
                method: 'POST',
                url: window.location.origin + '/API/List',
                data: formData,
                headers: {
                    'Content-Type': 'multipart/form-data',
                    "RequestVerificationToken": document.forms[0].querySelector('input[name="__RequestVerificationToken"]').value,
                }
            }).then(response => {
                if ( response.status == 401 || response.status == 402 || response.status == 403 ) {
                    window.location.href = response.headers.expiredtokenredirecturi;
                    return resolve(null);
                }
                return resolve( response.data );
            }).catch(error => {
                console.log( `Error [itemsChildren:axios]`, error );
                resolve( response.data );
            });
        });
    }
}

使用Async/Await

computed: {
    async itemsChildren() {
        if ( this.parentReview == null ) return null;

        const formData = new FormData();
        formData.append('ID', this.parentReview["ID"]);

        try {
            const response = await axios({
                method: 'POST',
                url: window.location.origin + '/API/List',
                data: formData,
                headers: {
                    'Content-Type': 'multipart/form-data',
                    "RequestVerificationToken": document.forms[0].querySelector('input[name="__RequestVerificationToken"]').value,
                }
            });
            if ( response.status == 401 || response.status == 402 || response.status == 403 ) {
                window.location.href = response.headers.expiredtokenredirecturi;
                return null;
            }
            return response;
        } catch ( error ) {
            console.log( `Error [itemsChildren:axios]`, error );
            return null;
        }
    }
}