1. 设置默认选中：

使用 default-checked-keys 属性，设置默认要选中的节点，以数组形式，如下：

<el-tree
   ref="treeRef"
   :data="data"
   show-checkbox
   node-key="id"
   :props="defaultProps"
   :default-checked-keys="[5]"
/>

2. 调用 Tree 实例对象的 getCheckedKeys 方法来获取选中的所有节点，如下：

const treeRef = ref();
const checkedId = ref([]);

function getCheckedId() {
  checkedId.value = treeRef.value?.getCheckedKeys();
}

完整代码如下：

<template>
  <div>
    <el-tree
      ref="treeRef"
      :data="data"
      show-checkbox
      node-key="id"
      :props="defaultProps"
      :default-checked-keys="[5]"
    />
    <el-button @click="getCheckedId">获取选中节点: {{ checkedId }}</el-button>
  </div>
</template>

<script setup>
const defaultProps = {
  children: "children",
  label: "label",
};
const data = [
  {
    id: 1,
    label: "Level one 1",
    children: [
      {
        id: 2,
        label: "Level two 1-1",
        children: [
          {
            id: 3,
            label: "Level three 1-1-1",
          },
          {
            id: 4,
            label: "Level three 1-1-2",
          },
        ],
      },
    ],
  },
  {
    id: 5,
    label: "Level two 1",
  },
];
const treeRef = ref();
const checkedId = ref([]);

function getCheckedId() {
  checkedId.value = treeRef.value?.getCheckedKeys();
}
</script>