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Looks like auth.isUserLoggedIn()
is not reactive, You can make it reactive by assigning its value to a reactive variable and then use that in your computed property. Can you give a try to this :
const loggedIn = ref(null)
const auth = useAuthMethod();
loggedIn.value = auth.isUserLoggedIn();
const isUserLoggedIn = computed(() => loggedIn.value)
Source:stackexchange.com