php - I want to global menu with Vue component which can change items when user login or logout

one text

I develop SPA service. Frontend is run by Vue.js and Backend is run by Laravel. I implement login function with laravel sanctum.

If user success login, vue hold value in local storage.

login() {
    axios.get("/sanctum/csrf-cookie").then(response => {
        axios
            .post("/api/login", {
                email: this.email,
                password: this.password
            })
            .then(response => {
                localStorage.setItem("auth", "true");
            })

    });

And if user logout, removeItem from localstorage.

logout() {
    axios
        .post("api/logout")
        .then(response => {
            this.user = "";
            this.localStorage = "";
            localStorage.removeItem("auth");
            this.$router.push("/login");
        })

},

I already implement preventing access to pages which are for login user by unlogin user.

resources/app.js

import VueRouter from 'vue-router';
window.Vue = require('vue').default;
import HeaderComponent from "./components/HeaderComponent";

import store from './store';


Vue.component('header-component', HeaderComponent);


Vue.use(VueRouter);

const router = new VueRouter({
    mode: 'history',
    routes: [
        {
            path: '/autoFunction',
            name: 'autoFunction',
            component: AutoComponent,
            meta: { authOnly: true }
        },

        {
            path: "/login",
            name: "login",
            component: LoginComponent,
            meta: { guestOnly: true }
        },


    ]
});

function isLoggedIn() {
    return localStorage.getItem("auth");
}

router.beforeEach((to, from, next) => {
    if (to.matched.some(record => record.meta.authOnly)) {
        if (!isLoggedIn()) {
            next("/login");
        } else {
            next();
        }
    } else if (to.matched.some(record => record.meta.guestOnly)) {
        if (isLoggedIn()) {
            next("/welcome");
        } else {
            next();
        }
    } else {
        next();
    }
});


const app = new Vue({
    el: '#app',
    router,
    store,
});

I also want to control global menu by user's login status.

resources/js/components/HeaderComponent.vue

<template>
    <div>
        <header class="l-header">
            <nav>
                <ul class="c-menu__ul" v-if="isLoggedIn()">
                    <a @click="logout">
                        <li>Logout</li>
                    </a>
                </ul>
                <ul class="c-menu__ul" v-if="!isLoggedIn()">
                    <router-link v-bind:to="{name: 'login'}">
                        <li>Login</li>
                    </router-link>
                </ul>
            </nav>
        </header>
    </div>
</template>
<script>
import axios from 'axios';
import store from "../store";

export default {
    data() {
        return {
            user: "",
        };
    },
    mounted() {
        axios.get("/api/getUserInfo").then(response => {
            this.user = response.data;
        });
    },

};
</script>

Is it possible to use app.js's methods in HeaderComponent.vue?

I also tried Vuex but I could't control global menu when user access external page and retuern.

resources/js/store.js

import Vue from 'vue';
import Vuex from 'vuex';

Vue.use(Vuex);

export default new Vuex.Store({
    state: {
        isLoggedIn: false,
    },
    mutations: {
        onUserLoginStatusChanged(state, isLoggedIn) {
            state.isLoggedIn = isLoggedIn;
        }
    },
    getters: {
        isLoggedIn(state) {
            return state.isLoggedIn;
        }
    }
});

resources/js/components/HeaderComponent.vue

            <nav>
                <ul class="c-menu__ul" v-if="this.$store.getters.isLoggedIn">
                    <a @click="logout">
                        <li>Logout</li>
                    </a>
                </ul>
                <ul class="c-menu__ul" v-if="!this.$store.getters.isLoggedIn">
                    <router-link v-bind:to="{name: 'login'}">
                        <li>Login</li>
                    </router-link>
                </ul>
            </nav>