`dlopen`'ing system libraries is an "easy" hack to try to maintain compatibility with wide variety of libraries/ABIs. It's barely used (I know only of SDL, Small HTTP Server, and now Godot).
Without dlopen (with regular dynamic linking), it's much harder to compile for older distros, and I doubt you can easily implement glibc/musl cross-compatibility at all in general.
Take a look what Valve does in a Steam Runtime:
- https://gitlab.steamos.cloud/steamrt/steam-runtime-tools/-/blob/main/docs/pressure-vessel.md
- https://gitlab.steamos.cloud/steamrt/steam-runtime-tools/-/blob/main/subprojects/libcapsule/doc/Capsules.txt