Nuxt component variable not updated - vue.js

Question

I wrote the following code for my navbar:
<template>
<div>
<div v-if="!$auth.loggedIn" data-tip="Login" class="tooltip tooltip-bottom">
<nuxt-link to="/login" class="btn btn-square btn-ghost">
<solid-login-icon class="w-6 h-6" />
</nuxt-link>
</div>
<div v-else class="flex items-stretch">
<a class="pr-2 btn btn-ghost rounded-btn"> Welcome, {{ this.$auth.user.username }}! 👋 </a>
<div data-tip="Logout" class="tooltip tooltip-bottom">
<button class="pr-2 btn btn-square btn-ghost" #click="logout()">
<solid-login-icon class="w-6 h-6" />
</button>
</div>
</div>
</div>
</template>
Which is include in the following login page:
<template>
<div class="h-screen shadow bg-base-200 drawer drawer-mobile">
<input id="my-drawer-2" type="checkbox" class="drawer-toggle" />
<div class="drawer-content">
<NavBar />
<div class="grid grid-cols-1 p-5 md:grid-cols-6">
<div class="col-span-1 md:col-span-2 md:col-start-3">
<div class="bg-white shadow card">
<div class="card-body">
<h2 class="text-left card-title">Login</h2>
<form #submit.prevent="userLogin">
<div class="form-control">
<label class="label">
<span class="label-text">Username</span>
</label>
<input
v-model="login.username"
type="text"
placeholder="Username"
class="input input-bordered"
/>
</div>
<div class="form-control">
<label class="label">
<span class="label-text">Username</span>
</label>
<input
v-model="login.password"
type="password"
placeholder="Password"
class="input input-bordered"
/>
</div>
<div class="mt-4">
<button type="submit" class="btn btn-primary btn-md">Login</button>
</div>
</form>
</div>
</div>
</div>
</div>
</div>
<SideBar />
</div>
</template>
<script>
export default {
data() {
return {
login: {
username: '',
password: '',
},
}
},
methods: {
async userLogin() {
try {
const response = await this.$auth.loginWith('local', { data: this.login })
} catch (err) {}
},
},
}
</script>
Upon loggin in with correct credentials the page keeps dispalying the "Login"-icon instead of the Welcome message.
I've tried to replace !$auth.loggedIn with loggedIn (coming from the data function) and with !this.$auth.loggedIn" but both don't seem to solve the issue