[clangd][NFC] Rename FSProvider and getFileSystem

Summary:
Clangd uses FSProvider to get threadsafe views into file systems. This
patch changes naming to make that more explicit.

Depends on D81920

Reviewers: sammccall

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

Tags: #clang

Differential Revision: https://reviews.llvm.org/D81998