Do buildtests on our public header files with C++ as well

This ensures that we don't mistakenly use C++ keywords anywhere public.

Related to #8313

(cherry picked from commit 9f27d4bf32c0465270e1922365b21825a0f7a42a)

Reviewed-by: Paul Dale <paul.dale@oracle.com>
(Merged from https://github.com/openssl/openssl/pull/8359)