cland-contexts extension issues

### Bug Description:

During testing of https://github.com/eclipse-cdt-cloud/cdt-cloud-blueprint/pull/67 I found the following two issues:

- When switching the build configuration before a C source file was opened, e.g. immediately after `clangd-contexts` example generation and `build.sh` execution, errors are thrown in relation to the clangd language server. The language server does not recover and the frontend must be restarted

- When generating both the `clangd-contexts` example and the `CMake` example, the cmake example is offered as an additional target for context switching. The context switching still works, however the context bar always shows "Build configuration: NONE"

### Additional Information

The clangd-contexts extension source can be found [here](https://github.com/eclipse-cdt-cloud/clangd-contexts).