This was ultimately a bug in Visual Studio. Visual Studio 17.11.5 onwards has a command to allow you to reset your extensions. From the bug report at visualstudio.com:

We have introduced a command in this release that should resolve the issue you’re experiencing. If you continue to face the same problem after updating or with a fresh installation, please follow the steps below:

• Close all running instances of Visual Studio.
• Open the Developer Command Prompt as an Administrator.
• Run the following command: devenv /updateconfiguration /resetExtensions
• Wait for the command to finish executing.
• Restart Visual Studio.