GKE Node.JS app: Error during WebSocket handshake

I am quite new to Google Kubernetes Engine, and just Kubernetes in general. I've created a "production-ish" Kubernetes cluster running my old Node.js app that's using socket.io. To help myself to do that I used Google's "Deploying a containerized web application" how-to after which I've set up a Load Balancer with an Ingress which would use a Managed Certificate by somewhat following another guide which is Using Google-managed SSL certificates (the Setting up the managed certificate part). This left me with a cluster using 1 pool with three instance groups, each using 1-2 nodes.

The backend was up and the frontends were able to connect to it correctly. The problem is with WebSockets and frontend getting an error WebSocket connection to 'wss://mycooldomain.com/socket.io/?EIO=3&transport=websocket&sid=afskjaisfhf-afasfoiaofis' failed: Error during WebSocket handshake: Unexpected response code: 400, which I've been trying to figure out all day.

The latter of the two guides I've been using mentions creating a Node Port and a Managed Certificate and then an Ingress which would link the two together. I have decided to create an Ingress with a different backend config for the load balancer in order to fix the problem:

apiVersion: cloud.google.com/v1beta1
kind: BackendConfig
metadata:
  name: my-cool-backendconfig
  namespace: my-cool-namespace
spec:
  timeoutSec: 60
  connectionDraining:
    drainingTimeoutSec: 30
  sessionAffinity:
    affinityType: "CLIENT_IP"

The reason for creating this is to try different values for timeouts in order to keep the WebSocket connection. I've also tried such values as timeoutSec: 20000 or drainingTimeoutSec: 3000. sessionAffinity part also came from many StackOverflow threads and GitHub issues.

So that config had to be applied on my NodePort:

apiVersion: v1
kind: Service
metadata:
  namespace: my-cool-namespace
  name: my-cool-nodeport
  labels:
    app: my-cool-app
  annotations:
    cloud.google.com/backend-config: '{"ports": {"80":"my-cool-backendconfig"}}'
spec:
  selector:
    app: my-cool-app
  type: NodePort
  ports:
    - protocol: TCP
      port: 80
      targetPort: 8080

And on my Ingress, if I understood correctly:

apiVersion: networking.k8s.io/v1beta1
kind: Ingress
metadata:
  namespace: my-cool-namespace
  name: my-cool-ingress
  annotations:
    kubernetes.io/ingress.global-static-ip-name: my-cool-global-ip
    networking.gke.io/managed-certificates: my-cool-certificate
    cloud.google.com/backend-config: '{"default": "my-cool-backendconfig"}'
spec:
  backend:
    serviceName: my-cool-nodeport
    servicePort: 80

After trying different values for timeouts, I've noticed that the Error during WebSocket handshake: Unexpected response code: 400 error does not necessarily happen on every socket.emit() and is rather variable, depending on, I guess whether the load balancer has allowed the connection (?).

Even if Google guides mention using larger timeout values, even the most obscene ones (timeoutSec: 20000 as I described above) don't really help establish stable WebSocket connections, because they end up throwing the error occasionally.

Looking at the problem from backend/frontend node apps standpoint, I've only gone as far as changing the socket.io config to try to establish websocket connection first before polling:

const server = http.createServer(app);
const io = require('socket.io').listen(server);
io.set('transports', ['websocket', 'polling']);

Which didn't help either.

How do I make it work without throwing the error every now and then?

Bonus question: I've noticed a lot of users with the same/similar problem use Nginx Ingress controllers, is that necessary for proper load balancing at all or is it only for real production environments?