[clangd] Cache .clang-tidy files again.

This cache went away in 73fdd998

This time, the cache is periodically validated against disk, so config
is still mostly "live".

The per-file cache reuses FileCache, but the tree-of-file-caches is
duplicated from ConfigProvider. .clangd, .clang-tidy, .clang-format, and
compile_commands.json all have this pattern, we should extract it at some point.
TODO for now though.

Differential Revision: https://reviews.llvm.org/D92133