OK, so I have installed webpack over npm. Additional I need some additional code in the vue.config.js, correct? Now my vue.config.js is:

const { defineConfig } = require('@vue/cli-service')
module.exports = defineConfig({
  transpileDependencies: true,
  configureWebpack: {
    devServer: {
      proxy: {
        '/api': {
          target: 'http://localhost:3080',
},},},},})

And edit the Endpoint to ...app.post("/api/signup",async (req,res)=>{... but its not work.

I get this error: Proxy error: Could not proxy request /api/signup from localhost:8080 to http://localhost:3080 (ECONNREFUSED).

Well if you need to run both on the same port you could first build your app so that you receive a dist directory or whatever your output directory is named and set up an express server that serves that app and otherwise handles your api requests

const express = require("express");

const path = __dirname + '/app/views/';
const app = express();

app.use(express.static(path));

app.get('/', function (req,res) {
  res.sendFile(path + "index.html");
});

app.get('/api', function (req,res) {
  // your api handler
}

app.listen(8080)