I don't know if this is the package you're using but whatever one you're using will be similar. In the readme it goes over two examples:

Server Example

In the server example they create a web socket server:

const WebSocket = require('ws');

const wss = new WebSocket.Server({ port: 8080 });

wss.on('connection', function connection(ws) {
  ws.on('message', function incoming(message) {
    console.log('received: %s', message);
  });

  ws.send('hello from the server!');
});

What this does is creates the listening socket server. It adds an event listener for message so when a client connects to the server that client can then send messages and that event handler will fire.

After that event listener it sends the string 'hello from the server!'. That send call will NOT fire the above event handler because this send call is happening on the server side of the socket. It is sending a message to be received on the client end of that socket.

Client Example (usually in browser)

const WebSocket = require('ws'); // omit this line if including ws via <script> tag

const ws = new WebSocket('ws://www.host.com/path');

ws.on('open', function open() {
  ws.send('hello from the client!');
});

ws.on('message', function incoming(data) {
  console.log(data);
});

This is a client script that connects to the socket server in the first example. It connects up and the 'connection' event will be raised on the socket server above. The socket server then calls ws.send('hello from the server!'); and our client script here sets up a listener for 'message' so it would fire and print out 'hello from the server!' to the browser console.

This client script also sets up an 'open' event handler which fires after a successful connection to the socket server. So it will fire and send 'hello from the client!' to the server. The server's handler for 'message' will fire and in the server's terminal you will see 'hello from the client!' print out.

In your example you're doing this from the server (your server side routes.js file)

wss.clients.forEach(function each(client) {
  if (client.readyState === WebSocket.OPEN) {
    client.send(data);
  }
});

What you're doing there is iterating over all connected clients that have successfully connected to the socket server and you're sending out a message to each one individually. This will still not fire the server-side on event handler for 'message' you set up on each socket when each one first connected. It will fire the handler on the client-side in the browser.

Edit based on your last comment above:

To do what you want you'd want something like this on the client:

myButton.onClick = function (e) {
  ws.send("Hey everyone! I'm Chev!");
};

Then on the server in the connection handler you'd want to set up a message handler like this:

wss.on('connection', function connection(ws) {
  ws.on('message', function incoming(message) {
    wss.clients.forEach(function each(client) {
      if (client !== ws && client.readyState === WebSocket.OPEN) {
        client.send(message);
      }
    });
  });
});

You can make message be an object instead of a string so you can perform different actions based on properties on that object but for the sake of simplicity I just made the server broadcast any message it receives to the rest of the server.

Notice the if statement checking to make sure we don't re-broadcast the message back to the same client who sent it.