Maybe the following solution is suitable for you:

Add Toast in App.vue and add a watch that checks for messages from the store

shop

import { createStore } from "vuex";

export default createStore({
    state: { errorMessage: "" },
    mutations: {
        setErrorMessage(state, payload) {
            state.errorMessage = payload;
        },
    },
    actions: {},
    modules: {},
    getters: {
            getErrorMessage: (state) => state.errorMessage,
    },
});

Then in any other component just update the message

store.commit("setErrorMessage", error.message);

This solution worked for me, but I'm not sure it's a good solution.

First: Export the application from main.ts

// main.ts
import {createApp} from 'vue';
import App from '@/App.vue';

import PrimeVue from 'primevue/config';
import ToastService from 'primevue/toastservice';

export const app = createApp(App);

app.use(PrimeVue);
app.use(ToastService);

app.mount('#app')

Second: Import the application and use the toast service of app.config.globalProperties

// myToastService.ts
import {ToastSeverity} from 'primevue/api';
import {app} from '@/main';

const lifeTime = 3000;

export function info(title: string = 'I am title', body: string = 'I am body'): void {
  app.config.globalProperties.$toast.add({severity: ToastSeverity.INFO, summary: title, detail: body, life: lifeTime});
};

export function error(title: string = 'I am title', body: string = 'I am body'): void {
  app.config.globalProperties.$toast.add({severity: ToastSeverity.ERROR, summary: title, detail: body, life: lifeTime});
};

Third: Import myToastService in the component.

// myTestToastComponent.vue