SOURCE

const arr = {
          subform41353:[
            {
              warehousing_apply_applicant_date:'1',
              warehousing_apply_department:'1'
            }
          ],
          subform57264:[
          {
              warehousing_apply_applicant_date2:'',
              warehousing_apply_departmen2:''
            }
          ]
}
// console.log(Object.entries(arr))
// const emptyElements = Object.entries(arr)
//   .flatMap(([objectName, elements]) => {
//     return elements.filter(element => Object.values(element).some(value => value === '')).map(() => objectName)
//   })
const emptyElements = [...Object.values(arr)]
  .flat()
  .filter(element => Object.values(element).some(value => value === ''))
console.log(emptyElements) // ["subform57264"]