Install ILSpy extension from official Visual Studio Marketplace or Open VSX.

On installation Visual Studio Code might ask to additionally install .NET Install Tool for Extension Authors, which is by design and intended.

On first start a .NET runtime is automatically downloaded in the background. This is necessary to use ILSpy decompilation engine.

The runtime is installed into a local VS Code directory and doesn't alter your system.

There is one exception: On Linux systems this process might also install some dependencies of the runtime, which could involve adding/updating some packages.