Вы можете использовать vanilla JS или loda sh funcntions - отфильтруйте массив и для каждого элемента проверьте, содержит ли массив data.interests
запрошенное слово.
Vanilla:
const home = [{"data":{"interests":["sports","travel","boxing"],"city":["x","y","z"],"name":"test1"},"count":["1","2"],"country":"CA"},{"data":{"interests":["painting","travel","dancing"],"city":["a","y","b"],"name":"test2"},"count":["1","3"],"country":"US"}]
const result = home.filter(o => o.data.interests.includes('dancing'))
console.log(result)
Loda sh:
const home = [{"data":{"interests":["sports","travel","boxing"],"city":["x","y","z"],"name":"test1"},"count":["1","2"],"country":"CA"},{"data":{"interests":["painting","travel","dancing"],"city":["a","y","b"],"name":"test2"},"count":["1","3"],"country":"US"}]
const result = _.filter(home, o => _.includes(o.data.interests, 'dancing'))
console.log(result)
<script src="https://cdnjs.cloudflare.com/ajax/libs/lodash.js/4.17.15/lodash.js"></script>