Can you SSH into your NAS and from the console try the following three commands and report here on the result:
telnet get.theturninggate.net 443
nc -zv get.theturninggate.net 443
curl http://get.theturninggate.net
(the first two are equivalent, but you may have only one of those tools available on the NAS)
The expected result is like this:
❯ telnet get.theturninggate.net 443
Trying 172.105.175.68...
Connected to get.theturninggate.net.
Escape character is '^]'.
^]
telnet> quit
Connection closed.
❯ nc -zv get.theturninggate.net 443
Connection to get.theturninggate.net port 443 [tcp/https] succeeded!
❯ curl http://get.theturninggate.net
Unable to specify controller and action: (, index)