Aetae

const {current}: {current: HTMLUListElement} = children;

const current = children.current as HTMLUListElement;

function unFlatten(array) {
  const childrenMap = Object.create(null);
	for(const item of array) {
    if(item.parent in childrenMap) 
      childrenMap[item.parent].push(item);
    else
      childrenMap[item.parent] = [item];  
    
    if(!childrenMap[item.id]) childrenMap[item.id] = []; 
    
    item.children = childrenMap[item.id];
  };
  return childrenMap[null]
}

function unFlatten(array) {
  const childrenMap = Object.create(null);
  const secondPass = [];
	for(const item of array) {
    if(item.parent in childrenMap) 
      childrenMap[item.parent].push(item);
    else
      childrenMap[item.parent] = [item];  
    
    if(item.id in childrenMap) 
      item.children = childrenMap[item.id];
    else
      secondPass.push(item)
  };	
  for(const item of secondPass) {
    if(item.id in childrenMap) 
      item.children = childrenMap[item.id];
  };
  return childrenMap[null]
}

function unFlatten(array) {
  const map = Object.create(null);
  const secondPass = [];
  for(const item of array) {
    map[item.id] = item;
    if(item.parent in map) {
      if('children' in map[item.parent])
        map[item.parent].children.push(item)
      else
        map[item.parent].children = [item];
    } else {
      secondPass.push(item);
    }
  };
  for(const item of secondPass) {
    if(item.parent in map) {
      if('children' in map[item.parent])
        map[item.parent].children.push(item)
      else
        map[item.parent].children = [item];
    }
  };
  return secondPass
}

function toObject(animals, titles, list) {
  animals = Object.fromEntries(animals);
  titles = Object.fromEntries(titles);
  return list.map(([animal, title, ...array], i) => ({
    id: i + 1, 
    title: titles[title], 
    animal: animals[animal], 
    array
  }));
}

toObject(arr1, arr2, arr3);

@Component
export default class Login extends Vue { 
  // ...
}
export default interface Login {
  $refs: {
     loginForm: any; // на самом деле не any, а интерфейс компонента, поддерживающий нужные методы
  }
}