[clang] [InstallAPI] Add support for C++ headers (PR #84403)

[Cyndy Ishida via cfe-commits]

cyndyishida wrote:

Looks like I made the mistake of deleting the target branch for PR: https://github.com/llvm/llvm-project/pull/83953 before updating it. Anyway, I applied @ributzka's forward declaration's suggestion. 

https://github.com/llvm/llvm-project/pull/84403