That’d be a question for the MusE authors to answer. Just because MusE runs inside an AppImage it is not magically loading things from different paths.
The documentation says:
A few sound samples are bundled with MusE to be used as metronome sound. If you have a favourite metronome sound it is also possible to copy this file as a .WAV to the metronome folder in the local configuration directory $HOME/.config/MusE/MusE/metronome , the supplied metronome samples are placed under the installation directory in share/muse-4.0/metronome .
share/muse-4.0/metronome is not a full path. Do they mean /usr/share/muse-4.0/metronome or $HOME/.local/share/muse-4.0/metronome?