This linked question provides an answer using std::exception_ptr, but requires both the legacy library and code using the library to be compiled with C++11 or later.

As noted in comments from @Botje, @jabaa, and @WeijunZhou, you may be able to get information from the legacy library itself, or can guess the exception type using casting.

Since the legacy library offers no clues and your guesses have not been successful, beyond a "general, unnamed exception", you are out of luck.