The problem

Some projects require newer C++ standards to build them. To keep the glibc dependency low you can build a newer GCC version on an older distro and use it to compile the project. This project however will now require a newer version of the libstdc++.so.6 library than available on that distro. Bundling libstdc++.so.6 however will in most cases break compatibility with distros that have a newer library version installed into their system than the bundled one. So blindly bundling the library is not reliable.

By the way, while this is primarily an issue with libstdc++.so.6 in some rare cases this might also occur with libgcc_s.so.1. That's because both libraries are part of GCC.

The solution

You would have to know the library version of the host system and decide whether to use a bundled library or not before the application is started. This is exactly what the patched AppRun binary does. It will search for usr/optional/libstdc++/libstdc++.so.6 and usr/optional/libgcc_s/libgcc_s.so.1 inside the AppImage or AppDir. If found it will compare their internal versions with the ones found on the system and prepend their paths to LD_LIBRARY_PATH if necessary. You should also put exec.so into usr/optional.