Boost up Token per minute for your AOAI Resources

Please take reference to this API management approach for well-architecture principle Azure OpenAI Service Load Balancing with Azure API Management
This sample policy source code demonstrate how to load balancing your backend with round robin manners APIM policy for load balancing

You can take reference of this obsoleted Function App approach for learning how AppGW rewrite rule works. Obsoleted Function App approach

Function App doesn't support data streaming as limitied by its serverless nature.