Automerge: [Github] Remove call to llvm-project-tests from libclang tests

This allows for removing llvm-project-tests.yml. This significantly
reduces the complexity of this workflow (including the complexity of
llvm-project-tests.yml) at the cost of a little bit of duplication with
the other workflows that were also using llvm-project-tests.yml.

Reviewers: tstellar, DeinAlptraum

Reviewed By: DeinAlptraum

Pull Request: llvm/llvm-project#153876

Author: boomanaiden154