Hello and thanks for reaching out. Session are bound to token provided during configure session

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token (required) A guest-generated UUID used to access the session. This value is arbitrary to Genesys Cloud, but it must be unique as it grants access to a specific session.

Session are bound to deployments.

I hope this answer your question

Does web messaging use solely the external participant to maintain Session Persistence, Asynchronous Communication and Message Threading? or does the Deployment ID also play a role?