[clangd] NFC: Cleanup unused headers and libraries

Summary: Extended version of D78843.

Reviewers: sammccall

Reviewed By: sammccall

Subscribers: mgorny, ilya-biryukov, MaskRay, jkorous, arphaman, kadircet, usaxena95, cfe-commits

Tags: #clang

Differential Revision: https://reviews.llvm.org/D79313