How to ensure that each instance of Shiny Python App connects to a seperate Google Cloud Run App?

Hi,

I have a Shiny Python App deployed on ShinyApps.io with a chat component. I also have a chatbot deployed on Google Cloud Run as a Flask App. When a Shiny App user writes something in the chat interface I send a request to the Flask App, retrieve the response, and display it on the chat component.

Both Shiny App and Flask App can handle multiple users. When multiple users sign in to different instances of Shiny App, I want each user to communicate with a different instance of Flask App, so that no two user will send request to the same instance of Flask App. What is the best method to achieve this?

Thanks