I have a node (express) server running at localhost:3000. On another hand, I have an HTML (client.html) file which is served by the server itself, on the route /client (the file is sent as the response).  
My goal here is to access another route, namely /test using an AJAX call on the client.html page (WHICH IS SERVED BY THE SAME SERVER). However, as it's quite obvious from the post, it isn't working.  
Not a duplicate: I have tried the solutions given in the following SO posts, so far, without success:
• jQuery Ajax request from local filesystem (Windows file:///) - though 
• ajax call not working when trying to send data to localhost:8000 from localhost
• Why doesn't adding CORS headers to an OPTIONS route allow browsers to access my API?
 
Here are my source codes.
server.js
const express = require("express")
const bodyParser = require("body-parser")
var app = express()
app.use(bodyParser.urlencoded({extended:false}));
app.use(bodyParser.json())
...
app.get('/', (req, res)=>{
    res.setHeader('Access-Control-Allow-Origin', '*')
    res.send('This server does not support GET requests.')
})
app.post('/test', (req, res)=>{
    res.setHeader('Access-Control-Allow-Origin', '*')
    res.send("response from /test")
})
var port = 3000
var server = app.listen(port)
client.html
<html>
    <script src="https://code.jquery.com/jquery-3.4.1.slim.min.js"></script>
    <script>
        function init(){
            $.ajax({
                url: 'http://127.0.0.1:3000/test',
                method: 'POST',
                contentType: 'application/x-www-form-urlencoded'
            }).done((data)=>{
                alert(data);
            });
        }
    </script>
    <body onload="javascript:init()">
    </body>
</html>
I have tried sending both a GET and a POST request but none of them worked.  
I have done this before, only not with nodejs. When I send a request from a Python script, using the requests library, the response is received, so the server seems to work just fine.  
FYI, I'm on Windows.
Where and/or what is the issue in?
 
    