Jest test does not find provided route

Question

Started working on a new application and decided to write tests from very early stage to avoid any future mistakes. However, little bit struggling I guess with setting up the Jest correctly. I made a follow on few tutorials and documentation, but the result is not the one I'm expecting. What I am trying to do is to make a basic test for creating a user, however I receive and error:

error: Error: cannot POST /register (404)

I get the point that the test can't find the endpoint /register, but I thought that is the point to keep server.js and app.js for supertest, because he will be smart enough to understand the path to this endpoint, which actually is: "/api/v1/auth/register". I want to mark that the registration process works fine trough postman.

Here is the app.js:

require("dotenv").config();
require("express-async-errors");

const express = require("express");
const app = express();

// routers
const authRouter = require("./src/routes/auth/auth.router");

// packages
const morgan = require("morgan");
const fs = require("fs");
const cookieParser = require("cookie-parser");

// middlewares
const errorMiddleware = require("./src/middlewares/errorMiddleware");

app.use(express.json());
app.use(cookieParser(process.env.ACCESS_TOKEN));
app.use(morgan("common", {
    stream: fs.createWriteStream("./src/utils/logs/logs.log", {
        flags: "a"
    })
}));

// endpoints
app.use("/api/v1/auth", authRouter);
app.use(errorMiddleware);

module.exports = app;

Here is the server.js:

const app = require("./app");

const PORT = process.env.PORT || 3000;
app.listen(PORT, () => {
    console.log(`Server is running on port ${PORT}...`);
});

Here is the auth.test.js:

const request = require("supertest");
const app = require("../../../app");

describe("POST /register", () => {
    it("Should create a new user", async () => {
        const response = await request(app).post("/register").send({
            email: "[email protected]",
            username: "superusername",
            password: "superpassword"
        });
        console.log(response); // I see here the 404 error.
    });
});

Not sure if it helps, but here is the router file:

const express = require("express");
const router = express.Router();

const {check} = require("express-validator");
const {registerUserController, loginUserController} = require("../../controllers/auth/auth.controller");

router.post("/register", [
    check("email").trim().not().isEmpty().isEmail(),
    check("username").trim().not().isEmpty().isString(),
    check("password").trim().not().isEmpty().isString().isLength({
        min: 6
    }).withMessage("Password has to be at least 6 characters long"),
    check("firstName").optional().trim().not().isEmpty().isString(),
    check("lastName").optional().trim().not().isEmpty().isString(),
    check("age").optional().trim().not().isEmpty().isNumeric().isInt({
        min: 0
    }).withMessage("Age can't be less than 0"),
], registerUserController);
module.exports = router;