[clangd] Move non-clang base pieces into separate support/ lib. NFCI

Summary:
This enforces layering, reduces a sprawling clangd/ directory, and makes life
easier for embedders.

Reviewers: kbobyrev

Subscribers: mgorny, ilya-biryukov, javed.absar, MaskRay, jkorous, arphaman, jfb, kadircet, usaxena95, cfe-commits

Tags: #clang

Differential Revision: https://reviews.llvm.org/D79014