Теряется объект пользователя при авторизации

import { auth, createUserWithEmailAndPassword, signInWithEmailAndPassword, signOut } from '@/lib/firebase/firebase';
 
export const useUserStore = defineStore('user', () => {
    const user = ref(auth.currentUser);
        console.log(user);
    console.log(user.value);
 
    async function register(email: string, password: string) {
        console.log('reg');
        try {
            const response = await createUserWithEmailAndPassword(auth, email, password);
            user.value = response.user;
        } catch (error: any) {
            const errorCode = error.code;
            const errorMessage = error.message;
        }
    }
 
    async function login(email: string, password: string) {
        console.log('login');
        try {
            const response = await signInWithEmailAndPassword(auth, email, password);
            user.value = response.user;
        } catch (error: any) {
            const errorCode = error.code;
            const errorMessage = error.message;
        }
    }
 
    async function logout() {
        console.log('logout');
 
        try {
            await signOut(auth);
        } catch (error: any) {
            const errorCode = error.code;
            const errorMessage = error.message;
        }
    }
 
    const isAuth = computed(() => !!user.value);
    const getUser = computed(() => user.value);
 
    return { user, register, login, logout, isAuth, getUser };
});