[llvm-branch-commits] [Github] Remove call to llvm-project-tests from libclang tests (PR #153876)

[Aiden Grossman via llvm-branch-commits]

https://github.com/boomanaiden154 created https://github.com/llvm/llvm-project/pull/153876

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.