[llvm-branch-commits] [Github] Remove call to llvm-project-tests.yml from mlir-spirv-tests.yml (PR #153871)

[Aiden Grossman via llvm-branch-commits]

https://github.com/boomanaiden154 created https://github.com/llvm/llvm-project/pull/153871

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.