Revert "Revert "[clang][extract-api] Use relative includes""

Reapply the change after fixing sanitizer errors.
The original problem was that `StringRef`s in `Matches` are pointing to
temporary local `std::string`s created by `path::convert_to_slash` in
the regex match call. This patch does the conversion up front in
container `FilePath`.

This reverts commit 2966f0fa.

Differential Revision: https://reviews.llvm.org/D124964