Unfortunately, we currently have no documentation/support for adding a second toolchain.
Also, mixing different toolchains is something hard to accomplish, and probably the OpenEmbedded documentation link that you shared is the way to go.
On the other hand, we can think about some workarounds (and all of them have pitfalls):
What if you try to statically link the dependencies to your application (including libc/libc++ here)? This way your application would be independent of the libs present in the module’s OS. Also, you will need to maintain two different build environments (one using Yocto, for your OS, and the other for your application).
Another way would be to get rid of the C++20 specific features on your application. You could take a look at whichever C++ revision (17, 14, 11, …) is compatible with the toolchain on BSP 2.8.7 and use only its features.
Get rid of the C++20 specific features isn’t an option. The application is an open-source project and I haven’t control over the C++ features. Statically link may be the easiest way to go.