I am currently level 60 and on "Matoya's Cave" in the main scenario.

I went to unlock the Gunbuster quest and it says that I need to have Shadowbringers installed and registered.

I had the starter edition on steam for years but actually started playing a couple months ago. I purchased Endwalker on Steam when I hit level 50 and wanted to get beyond that. Everyhting seemed fine until I tried to do this quest.