In combination with my revised article on Vuetify's dark mode state

DarkModeExample.vue

<template>
    <v-btn icon @click="toggleDarkMode">
        <v-icon>mdi-theme-light-dark</v-icon>
    </v-btn>
</template>

<script>
export default {
    name: "Example",
    methods: {
        toggleDarkMode: function() {
            this.$vuetify.theme.dark = !this.$vuetify.theme.dark;
            localStorage.setItem("darkTheme", this.$vuetify.theme.dark.toString());
        }
    },
    mounted() {
        const theme = localStorage.getItem("darkTheme");
        if (theme) {
            if (theme === "true") {
                this.$vuetify.theme.dark = true;
            } else {
                this.$vuetify.theme.dark = false;
            }
        } else if (
            window.matchMedia &&
            window.matchMedia("(prefers-color-scheme: dark)").matches
        ) {
            this.$vuetify.theme.dark = true;
            localStorage.setItem(
                "darkTheme",
                this.$vuetify.theme.dark.toString()
            );
        }
    }
}
</script>