Sending Array from server to client NodeJs

Backend

First off, I strongly advise you to read the express docs or some tutorials. I refactored your code. Change the import methods the way you want, I believe you use require.

import express from "express";
import path from "path";
const app = express();

// The backend shouldn't be running 24/7. You should store this data in
// a database (SQL/MongoDB/anything else), or at least in a JSON file.
const avails = Array(3).fill(0);

// Parse JSON bodies for POST requests
app.use(express.json());

// Logger. I advise you to check out "morgan" on npm,
// it's the best-known logger for express:
// app.use(morgan("dev"))
app.use((req, res, next) => {
    console.log(req.path);
    next();
});

// You should move "website.html" to "public/website.html"
// Every file in "public/" will be staticly accessible.
// If I understood correctly, there's other files you want to serve.
// Put them there too.
app.use("/", express.static(path.join(__dirname, "public")));

// Use get, not post! You're not creating data, but fetching data
app.get("/avails", (req, res) => res.json(avails));

// This route is to update the status of a room. Security-wise,
// it isn't very good as the array can be completely destroyed by a 
// remote client, but it works. Example: 
// POST /rooms/2/status { value: 2 }
app.post("/rooms/:room/status", (req, res) => {
    if (typeof req.body["value"] !== "number")
        return res.status(400).json({ message: "No valid new value is specified" });
    const room = +req.params["room"];
    const newStatus = req.body["value"];
    avails[room] = newStatus;
    console.log("new avails:", avails);
    res.json({ message: "Success!", avails });
});

// Connect to port 3000
app.listen(3000, () => console.log("Server is ready"));

Deprecation warnings

Now, a quick note on the things you're using while you shouldn't. I'm adding this because the above code doesn't replace the methods, but avoids them.

1. Use express properly please, but I think you got it by now:
   • Use the express.static() middleware whenever you can for static files
   • Use middlewares.
   • Use properly the req and res objects. Simplicity is your friend.
2. url.parse is deprecated, you should use new URL(), and get the search params from its searchParams property.
3. fs.exists is also deprecated.

Frontend

You can make requests to your backend using the fetch API.

const root = "http://localhost:3000"; // Or whatever your backend URL is

async function getAvails() {
    const url = new URL("/avails", root).href;
    const body = await fetch(url).then(res => res.json());
    return body.data;
}

async function setRoomState(room, value) {
    const url = new URL(`/rooms/${room}/status`, root).href;
    const body = await fetch(url, { method: "POST", body: { value } }).then(res =>
        res.json()
    );
    // Returns new avails
    return body.avails;
}

// Use these functions wherever you want

Side note about your project

If your project is about counting the number of people in a room, maybe you'll want to check out an old (small) project of mine, echo. Here's echo-mum, the backend written in TypeScript, maybe it'll help.