所需的结构不能仅由数组表示;使用对象代替键-值对。你可以使用Array#reduce将元素按状态分组到一个对象中。

let data=[{Name:"House 1",Details:[{Materials:"Door",Status:"Delivered"},{Materials:"Closet",Status:"Pending"},{Materials:"Chair",Status:"Pending"},{Materials:"Kitchen",Status:"Delivered"},{Materials:"Door Knob",Status:"Delivered"}]},{Name:"House 2",Details:[{Materials:"Cabinet",Status:"Delivered"},{Materials:"Kitchen",Status:"Delivered"},{Materials:"Door",Status:"Ongoing"},{Materials:"Chair",Status:"Ongoing"},{Materials:"Window",Status:"Cancelled"}]},];
let res = Object.fromEntries(data.map(o => [o.Name, o.Details.reduce((acc, curr) => {
  (acc[curr.Status] ??= []).push(curr.Materials);
  return acc;
}, {})]));
console.log(res);

这看起来和你要的很接近。都是数组。

let data=[
    {
        Name: 'House 1', 
        Details:[
            {Materials: 'Door', Status: 'Delivered'},
            {Materials: 'Closet', Status: 'Pending'},
            {Materials: 'Chair', Status: 'Pending'},
            {Materials: 'Kitchen', Status: 'Delivered'},
            {Materials: 'Door Knob', Status: 'Delivered'}
        ]
    },
    {
        Name: 'House 2', 
        Details:[
            {Materials: 'Cabinet', Status: 'Delivered'},
            {Materials: 'Kitchen', Status: 'Delivered'},
            {Materials: 'Door', Status: 'Ongoing'},
            {Materials: 'Chair', Status: 'Ongoing'},
            {Materials: 'Window', Status: 'Cancelled'}
        ]
    }
];
let newData=[];
for(let i in data){
    let delivered=data[i].Details.filter(e=>{if(e.Status==="Delivered")return true});
    let Pending=data[i].Details.filter(e=>{if(e.Status==="Pending")return true});
    let Ongoing=data[i].Details.filter(e=>{if(e.Status==="Ongoing")return true});
    let Cancelled=data[i].Details.filter(e=>{if(e.Status==="Cancelled")return true});
    let t=[data[i].Name,[],[],[],[]];
    for(let x in delivered){
        t[1].push(delivered[x].Materials);
    }
    for(let x in Pending){
        t[2].push(Pending[x].Materials);
    }
    for(let x in Ongoing){
        t[3].push(Ongoing[x].Materials);
    }
    for(let x in Cancelled){
        t[4].push(Cancelled[x].Materials);
    }
    newData.push(t);
}
console.log(newData);