[Github] Remove call to llvm-project-tests.yml from mlir-spirv-tests.yml
This will eventually allow for removing llvm-project-tests.yml. This
should significantly reduce the complexity of this workflow (including
the complexity of llvm-project-tests.yml) at the cost of a little bit of
duplication.
Reviewers: IgWod-IMG, kuhar
Reviewed By: kuhar
Pull Request: https://github.com/llvm/llvm-project/pull/153871