[clangd] Change ParseInputs to store FSProvider rather than VFS

Summary: This ensures ParseInputs provides a read-only access to FS.

Reviewers: sammccall

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

Tags: #clang

Differential Revision: https://reviews.llvm.org/D81173