That is... strange. ModBuddy should definitely have a few templates. I'd first try uninstalling and reinstalling it. If that fails, right click the Civ6 Development Tools in Steam, select "Properties", go to the "Local Files" tab at the top, and click "Verify integrity of tool files..."
If all that fails, delve a bit deeper. Again, make like you're going to verify integrity, but this time, click "Browse local files..."
This should bring you to where the Dev Tools installed, which is where everything else in Steam tends to install--Program Files/Steam/steamapps/common. Once you're in the Civ6 SDK folder (you should be already), navigate through folders in the order of /ModBuddy/Extensions/Application.
In the Application folder, there should be two further folders (along with a bunch of other stuff), called ProjectTemplates and ItemTemplates. The templates you're referring to are in ProjectTemplates. If you see that folder, go inside it, to Civ6ModProject/1033. There should be 6 .zip files there (which are the templates). If they're not there, then that's why you can't see them when you start up ModBuddy.
If you'd like, I can upload my own (since I have access to them), but obviously downloading what I have is a lot less secure than downloading from Steam, so that's why I encourage you to uninstall/reinstall/verify integrity (i.e. exhaust other options) before I give you mine.