Cannot able to use firebase firestore increment(1) using vue3 - firebase

Question

I want to make an increment on firestore database entry, as I press the everything works fine: I can create database to the server, and the aollcation of the names are correct, until I create an increment on Add Category Infomation.
this is my firebase console so far, it add two entry separately.
enter image description here
enter image description here
This is the complete code below:
<template>
<div class="CategoyAddAll">
<from #sumbit.prevent="addCategory">
<div class="grid gird-cols-2 gap-2">
<div><label>Category Name</label></div>
<div><input ref="category_enter" type="text" required/></div>
</div>
</from>
<button #click="createCategory" class="btn btn-info" >Add Category Information </button>
<br>
<br>
</div>
</template>
<script>
import { db, auth, fv } from "#/firebase.js";
import { create } from "domain";
import { collection, addDoc, FieldValue, DocumentReference } from "firebase/firestore";
export default{
name: 'CategoyAddAll',
setup() {},
data(){
return{
all_category: [],
client:{
category_fullname: null,
category_counter: null,
}
}
},
components: {},
methods:{
//
async createCategory(){
console.log("[CategoryAddAll] create new Category.");
const db_id = firebase.firestore();
const get_id = db_id.collection('all_categorys').doc();
const category_id = get_id.id;
console.log("[CategoryAddAll] id.");
const increment = firebase.firestore.FieldValue.increment(1); //always "1"
console.log("[CategoryAddAll] id2.");
const ref = collection(db, 'all_categorys');
const ref2 = db_id.collection('all_categorys'); //ignore this
//get_id.update({ reads: increment });
//https://fireship.io/snippets/firestore-increment-tips/
console.log("[CategoryAddAll] update incremented. " + this.$refs.category_enter.value);
const obj_ref ={
category_fullname : this.$refs.category_enter.value,
}
const doc_ref = await addDoc(ref, obj_ref);
const batch = db_id.batch();
batch.set(get_id, {category_increment: increment}, { merge: true }); //incrment in seperate value, always 1
batch.commit();
//get_id.update({ category_increment: increment });
},
}
}
</script>
I install Firebase correclt and it runs and able to add data, how come the "const increment = firebase.firestore.FieldValue.increment(1)" won't work? any help would be helpful? thank you.
I want to be like this below:
{
category_fullname: test_FULLname
category_increment : 11 //12 13 so on.
}
The category_increment should be based on how many entry I do. Lat's say if I have 10 category inside the database, the next entry of category_increment should be 11, even if there this an element delte, it will also become 12 and so on...