Hmmm.
This is not complicated. Straight forward, standard SQL connection string. Your system (REST API) to connect to a relational database.
I can connect to this db server db remotely from other locations no problem at all, just not from Appery.
I have added your ip addresses to the firewall allthough I should not need to as I allow TCP on port 1433 from anywhere. I have even switched the firewall off.
(IP ADDRESS CHANGED ON IMAGE FOR SECURITY PURPOSES but this illustrates what I did. Simple standard remote SQL connection.
I have a suspicion that you cant accept instances after the ip address? As I could get this to work to my AZURE server which does not have instances.
It is SQL 2016 on WIndows Server 2012 R2