A few days ago Microsoft announced the general availability of Virtual Network service endpoints for Azure Database for MySQL and PostgreSQL in all regions where the service is available for General Purpose and Memory Optimized servers.
Turning on VNet service endpoints do not override firewall rules that you have provisioned on your Azure Database for MySQL or PostgreSQL. Both continue to be applicable.
To ensure connectivity, you can preemptively specify VNet firewall rules before turning on service endpoints by using IgnoreMissingServiceEndpoint flag.
As part of the general availability, Microsoft will also support service endpoints for App Service Environment subnets deployed into your VNets.2