Can't connect to Cloud SQL using shinyproxy on Kubernetes

How can I make each instance of my shinyproxy app on Kubernetes connect to google cloud sql database?

I deployed an app on Kubernetes using shinyproxy. I used the documentation (and some examples, like https://medium.com/@rohitsrmuniv/using-shinyproxy-with-kubernetes-eba5bd06230) to create a kubernetes sidecar so each instance is created on a new pod. The app works except for the part that tries to connect to my database on Google Cloud SQL.

I followed their documentation (https://cloud.google.com/sql/docs/mysql/connect-kubernetes-engine) and created another sidecar with cloud SQL proxy. It appears to work: the deployed app has three pods: shiny app, shinyproxy (sidecar) and cloud proxy (sidecar). However, new instances of the app can’t connect to the database as they don’t have their own cloud proxy sidecar to manage the connection.

Is there another way to connect to the database? Or should I add new specs on application.yaml ou deployment.yml?