Allow changing Chat Profile for an existing thread

[DmitriyAlergant]

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Is your feature request related to a problem? Please describe.

Currently, changing Chat Profile forcefully triggers a New Chat creation. It does not seem to be possible to change a Chat Profile for an existing thread. Unless I missed anything?

In applications where Chainlit is used to simulate a simplified ChatGPT/OpenWebUI environment and Chat Profiles are used as Model Selectors, this kinda limits the user capabilities where otherwise in other applications a user is able to change a model within an existing chat thread.

Describe the solution you'd like

Allow changing Chat Profiles on an existing thread (with persistence) without creating a new chat.