I have built a test project on GCP.
I had a machine with external IP, google cloud SQL instance and I was able to connect between the two easily.
Then I've added a load balancer. I also opened ports to allow traffic from the compute engine to cloud SQL and also ensured I have whitelisted the traffic on the cloud SQL for the load balancer public IP.
However, I am no longer able to connect from the compute engine to the MySQL instance.
I have a feeling this is related to firewall after adding an LB, but I am unsure.