On my machine, I got SSDT as a downloaded extension for Visual Studio (EE). Menu: Extensions, Manage Extensions, search for ssdt.
The files for that extension were downloaded to C:\Program Files (x86)\Microsoft Visual Studio\2019\Enterprise\Common7\IDE\Extensions\Microsoft\SQLEditor
Visual studio still wasn't looking for it in the right place because my devenv.exe.config wasn't looking in that path. Use notepad to edit C:\Users\[UserName]\AppData\Local\Microsoft\VisualStudio\16.0_d6d04886\devenv.exe.config
. The config contained xml element: \configuration\runtime\assemblyBinding\probing:privatePath
which seems to contain paths where Visual Studio searches for extensions. I and added "Extensions\Microsoft" to the privatePath attribute. Saved. Restarted Visual Studio 2019 EE.