HPA with websocket server

We have a websocket server running in AKS cluster that maintains websocket connections with service running on Edge. The timeout ( > 2 hours ) for this connection is configurable and the client reconnects after this configured time.
Though the number of connections remain constant the messages transferred varies. Since the connections are persistent and long term in case the HPA triggers we need a way to redistribute the connections when new pods are added. What would be the best approach to handle this ??

Cluster information:

Kubernetes version: 1.18.17
Cloud being used: Azure
Installation method: Helm
Host OS: Photon OS
CNI and version:
CRI and version:

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