Hi @SR-7559 From my understanding, if you create a Flexible server on a VNET (without Public access) as you mentioned above, you will not see IP addresses under the networking tab as shown below.
But if you create a Flexible server with public access you will see the below option under the networking tab in the Azure Portal
If you server is in VNET, it can only connected from VM within the VNET. If flexible server is outside the VNET, it can be connected anywhere as long as the IP is allowed in the firewall rules. In both cases, would recommend to use FQDN to connect , not the IP.
Please also check this blog, it will be very helpful to understand the Private access integration DNS configuration patterns for Azure PostgreSQL and also MYSQL flexible server
Fell free to reach out if you still need further help
Regards,
Oury