Hey, I saw your chat post. Just wanted to say that I am 99.99999% sure that nothing but the Global Link in SM and USUM is shut down. GTS, Wonder Trade, multiplayer battling, Pokemon Bank, and other WiFi-related things should be working as normal unless you have a problem with your own DS or WiFi. Here's some info about Global Link (which is completely unrelated to GTS, trading, battling, etc.), and some info about those things still being functional:
https://bulbapedia.bulbagarden.net/wiki/Pokémon_Global_Link#Generation_VII
https://www.gamespot.com/articles/pokemons-global-link-service-is-shutting-down-but-/1100-6471729/
Hope I helped!