how to remove an array item from firestore using JavaScript?

I’m trying to add a delete button to my page. the event listener callback is working properly except for the updateDoc function.

await updateDoc(doc(dataBase, 'users', `${auth.currentUser.uid}`), {
     [`${col}.books`]: arrayRemove(`${bookToDelete}`)
}).then(()=>{
      // fulfilled
      console.log('book deleted')
      }, ()=>{
      // rejected
      console.log('promis rejected')
})

Col is the object that contains the books array. In the console it always prints book deleted, but in the firestore console, nothing changes. this is a screenshot of the database.enter image description here

I would really appreciate any help and thank you.