[Feature Request] Private Streaming and Backend APIs

## Describe the solution you'd like

Create a deployment option that bundles all backend

## Why the solution needed

Many customers require any and all internal usage of generative AI to transit their corporate network. At present the use of HTTP API and Websocket API means that using this solution as-is is a non-starter.

Options include:
- Converting HTTP API to a REST API, thus allowing use of [private API](https://docs.aws.amazon.com/apigateway/latest/developerguide/apigateway-private-apis.html) ([done](https://github.com/ggallo/bedrock-claude-chat/commit/5f91571b6b0bea7a7937088ff9cfaff55d9c38b8))
- Convert the Streaming API to an ECS Service using [websockets](https://websockets.readthedocs.io/en/stable/)

## Additional context

You can reach me on Slack

## Implementation feasibility

Are you willing to discuss the solution with us, decide on the approach, and assist with the implementation?

- [X] Yes!
- [ ] No