JSFiddle - React, Tailwind, and code Playground

JavaScript

const excludeItems = (arrayOfSearchItems, arrayOfObjects) => {
    return arrayOfObjects.filter(obj => {
    	return obj.storage.every(storageItem => {
            return arrayOfSearchItems.includes(storageItem) === false;
        });
    });
}

const arrayOfObjects = [
  { 
    name: 'box1',
    storage: ['car', 'goat', 'tea']
  },
  {
    name: 'box2',
    storage: ['camel', 'fox', 'tea']
  }
];

const arrayOfSearchItems = ['goat', 'car', 'oranges'];

const filteredArray = excludeItems(arrayOfSearchItems, arrayOfObjects);
console.log(filteredArray);