20222/7/29 做了一些优化。
效果图：

HTML：

<template>
  <div>
    <div class="nav">
      <h2>todoList</h2>
    </div>

    <div class="main">
      <div>
        <div class="main-top">
          <input
            type="text"
            v-model="addItem"
            class="add-input"
            @keyup.enter="handleAddClick()"
          /><button class="add-btn btn" @click="handleAddClick()">添加</button>
        </div>
        <!-- select item's status-->
        <div class="selection">
          <button
            class="btn"
            v-for="(item, index) in statusList"
            :class="{ 'item-click': item.status }"
            @click="handleSelectStatus(item)"
            :key="index"
          >
            {{ item.name }}
          </button>
        </div>
      </div>

      <!-- show list -->
      <div>
        <h3>{{ title }}</h3>
        <ul>
          <li v-for="(todoItem, index) in showList" :key="index" class="itemLi">
            <input
              type="checkbox"
              v-model="todoItem.done"
              @click="handleCheckItem(todoItem, todoItem.done)"
            />
            <span :class="setDeleteClass(todoItem.done)">
              {{ todoItem.content }}
            </span>
            <a href="#" @click="handleDeleteClick(index)">
              <img src="../assets/trash.svg" alt="" />
            </a>
          </li>
        </ul>
      </div>
    </div>
  </div>
</template>

js：

<script>
export default {
  data () {
    return {
      title: "全部事项",
      msg: "todo list",
      addItem: "",
      todoList: [],
      showList: [],
      statusList: [
        {
          name: '全部',
          value: 'all',
          status: true
        },
        {
          name: '待办',
          value: "todo",
          status: false
        }, {
          name: '已完成',
          value: 'done',
          status: false
        },
      ],
      currentSelectStatusItem: {} //用来暂存当前showList的状态
    }
  },
  created () {
    this.init();
  },
  methods: {
    init () {
      if (localStorage.getItem('todoItem')) {
        if (JSON.parse(localStorage.getItem('todoItem')).length > 0) {
          this.todoList = JSON.parse(localStorage.getItem('todoItem'))
          this.showList = this.todoList
          console.log(' init todo list', this.todoList)
        }
      }
    },
    handleAddClick () {
      if (this.addItem) {
        let item = { content: this.addItem, done: false }
        this.todoList.push(item)
        localStorage.setItem('todoItem', JSON.stringify(this.todoList))
        this.addItem = ''
        this.showList = this.todoList
        this.handleSelectStatus(this.statusList[0]) //添加完成后显示“全部”列表
      } else {
        alert('请输入内容')
      }
    },
    handleCheckItem (item, isDone) {
      item.done = !isDone
      localStorage.setItem('todoItem', JSON.stringify(this.todoList))
      this.handleSelectStatus(this.currentSelectStatusItem)
    },
    //选择全部、未完成、已完成并显示对应事项
    handleSelectStatus (item) {
      this.currentSelectStatusItem = item
      let statusValue = item.value
      this.showList = []
      for (let i = 0; i < this.statusList.length; i++) {
        this.statusList[i].status = false
      }
      switch (statusValue) {
        case 'done': this.title = "全部事项"
          this.title = "已完成"
          item.status = true
          for (let i = 0; i < this.todoList.length; i++) { //未完成
            if (this.todoList[i].done == true) {
              this.showList.push(this.todoList[i])
            }
          }
          break;

        case 'todo': this.title = "待办事项"
          item.status = true
          for (let i = 0; i < this.todoList.length; i++) {
            // 判断事项是否完成，是：true，否：false
            if (this.todoList[i].done == false) {
              this.showList.push(this.todoList[i])
            }
          }
          break;
        default: this.title = "全部事项"
          this.showList = this.todoList
          item.status = true
      }

    },
    handleDeleteClick (index) {
      this.todoList.splice(index, 1)
      localStorage.setItem('todoItem', JSON.stringify(this.todoList))
    },
    setDeleteClass (isDone) {
      if (isDone) {
        return 'delText'
      } else {
        return ''
      }
    }
  }
}
</script>

css:

<style>
li {
  list-style: none;
  color: #666;
  height: 50px;
  line-height: 50px;
  border-bottom: 1px solid #eeeeee;
}
ul {
  padding: 0;
}
.btn {
  height: 30px;
  width: 80px;
  color: #fff;
  border: none;
  border-radius: 3px;
}
.delText {
  text-decoration: line-through;
  color: rgb(170, 167, 167);
}
.itemLi a {
  float: right;
  text-decoration: none;
  color: #666;
  margin-right: 5px;
  width: 15px;
  height: 15px;
}
.main,
.nav {
  max-width: 800px;
  padding: 0 20px;
  margin: 0 auto;
}
.selection {
  display: flex;
  justify-content: flex-end;
  margin: 10px 0;
}
.selection .btn {
  display: inline-block;
  margin: 0 5px;
  width: 70px;
  color: #666;
}
.selection .btn:hover{
  cursor: pointer;
}
.selection .item-click {
  background-color: #f5750cdd;
  color: #fff;
}

.add-input {
  width: 85%;
  height: 25px;
  border-radius: 5px;
  border: 1px solid #cdcdcd;
}
.main-top {
  position: relative;
}
.add-btn {
  position: absolute;
  right: 5px;
  background-color: #009687e2;
}
</style>