you use await first see async function is nesscesssry

addDoc(collection(db, 'Institute', 'Private', 'College'), { name:"tunio" })

this is working for me

try this one for add subcollections in firebase v9

`function uploadData() {
    var id = 'id_' + Math.random().toString(36).substring(2) + (new Date()).getTime().toString(36); //create id for uniqness

    setDoc(doc(db, "Institute", `college`, `city`, `${id}`), {
        Name: "CAted college"
    })}`

//if you not use id set primary as name then no need to use id only write "name" of sugeesttion that unique for data base instead of id

It seems you were in the right direction but I would recommend checking how to reference subcollections and then using that reference to write data into it.

It won't hurt to check your imports and dependencies as well.

import  { doc } from "firebase/firestore";  

const messageRef = doc(db,  "rooms",  "roomA",  "messages",  "message1");

This translated to your project would be:

const notesRef = doc(db, 'users', idDoc, 'notes'); 

Next, you need to check the Add a document section as well. The code you are using as a reference applied to your app would create a new note with an auto-generated id. In the reference, "cities" would correspond to your "notes" reference.

Finally, if you substitute this, it would look like this:

const noteRef = await addDoc(collection(db, notesRef), {
    title: noteTitle,
    body: 'comentario por defecto.',
    timestamp: serverTimestamp() // You also had an extra coma here
});
console.log("Note written with ID: ", noteRef.id);

The console log is optional