refactor(lambda): simplify streaming handler and remove type workaround

[albidoo]

found this while going through codebase

declare const awslambda: {
  streamifyResponse: (
    handler: (
      event: LambdaEvent,
      responseStream: NodeJS.WritableStream,
      context: LambdaContext
    ) => Promise<void>
  ) => Handler
  HttpResponseStream: {
    from: (
      stream: NodeJS.WritableStream,
      metadata: { statusCode: number; headers: Record<string, string>; cookies: string[] }
    ) => NodeJS.WritableStream
  }
}

This ensures
streamHandle
is fully type-safe.

The author should do the following, if applicable

• Add tests
• Run tests
• bun run format:fix && bun run lint:fix to format the code
• Add TSDoc/JSDoc to document the code