[clang-tools-extra] [clangd] Turn `Path` and `PathRef` into classes (PR #136439)

[Nathan Ridge via cfe-commits]

HighCommander4 wrote:

@kadircet or @llvm-beanz, would you be able to help by reviewing this? It's addressing an issue affecting a lot of users (https://github.com/clangd/clangd/issues/108), or at least making progress towards addressing that issue.

https://github.com/llvm/llvm-project/pull/136439