[clangd] Use AsyncTaskRunner in BackgroundIndex instead of std::thread

Summary:
To unify the way we create threads in clangd.
This should simplify landing D50993.

Reviewers: kadircet

Reviewed By: kadircet

Subscribers: MaskRay, jkorous, arphaman, jfb, cfe-commits

Tags: #clang

Differential Revision: https://reviews.llvm.org/D61724

llvm-svn: 360332